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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(caret)## Loading required package: lattice
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## liftlibrary(lubridate)
library(dplyr)
library(ggplot2)
library(rpart)
library(caret)
library(rpart.plot)
library(tidyr)
library(rattle)## Loading required package: bitops
## Rattle: A free graphical interface for data science with R.
## Version 5.5.1 Copyright (c) 2006-2021 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.library(glmnet)## Loading required package: Matrix
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## Loaded glmnet 4.1-8library(FSelectorRcpp)
library(e1071)
library(randomForest)## randomForest 4.7-1.2
## Type rfNews() to see new features/changes/bug fixes.
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## Attaching package: 'randomForest'
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## importance
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## marginlibrary(conflicted)
conflicts_prefer(dplyr::filter)## [conflicted] Will prefer dplyr::filter over any other package.conflicts_prefer(dplyr::lag)## [conflicted] Will prefer dplyr::lag over any other package.match_data <- read.csv("match_data.csv")match_data <- match_data %>%
filter(suspended == "False" & stopped == "False")match_data <- match_data %>%
mutate(
match_start_datetime = ymd_hms(match_start_datetime),
current_time = ymd_hms(current_time),
final_score = as.factor(final_score),
result = as.factor(result)
)match_data <- match_data %>%
mutate(
P_home = 1 / `X1`,
P_draw = 1 / X,
P_away = 1 / `X2`
)
match_data <- match_data %>%
mutate(
total_prob = P_home + P_draw + P_away,
P_home_norm = P_home / total_prob,
P_draw_norm = P_draw / total_prob,
P_away_norm = P_away / total_prob
)matches_with_too_many_na <- match_data %>%
group_by(fixture_id) %>%
summarise(
X1_na_count = sum(is.na(X1)),
X2_na_count = sum(is.na(X2)),
X_na_count = sum(is.na(X))
) %>%
filter(
X1_na_count > 10 | X2_na_count > 10 | X_na_count > 10
)
matches_with_too_many_na## # A tibble: 0 × 4
## # ℹ 4 variables: fixture_id <dbl>, X1_na_count <int>, X2_na_count <int>,
## # X_na_count <int>match_data_filled <- match_data %>%
group_by(fixture_id) %>%
mutate(across(
where(is.numeric), # Only apply to numeric columns
~ {
# 1. If all values are NA, fill with 0
if (all(is.na(.))) {
return(rep(0, length(.)))
}
# 2. If there are NA values at the start, fill with 0
filled <- replace_na(.x, 0)
# 3. Apply both forward and backward filling
filled <- zoo::na.locf(filled, na.rm = FALSE) # Forward fill
filled <- zoo::na.locf(filled, fromLast = TRUE, na.rm = FALSE) # Backward fill
# 4. Fill remaining NA values at the end with the last non-NA value
filled <- replace_na(filled, last(filled[!is.na(filled)]))
return(filled)
}
)) %>%
ungroup()
head(match_data_filled)## # A tibble: 6 × 113
## fixture_id halftime current_time half_start_datetime
## <dbl> <chr> <dttm> <chr>
## 1 19172016 1st-half 2024-08-09 18:11:36 2024-08-09 18:01:37
## 2 19172016 1st-half 2024-08-09 18:27:30 2024-08-09 18:01:37
## 3 19172016 1st-half 2024-08-09 18:28:25 2024-08-09 18:01:37
## 4 19172016 1st-half 2024-08-09 18:29:32 2024-08-09 18:01:37
## 5 19172016 1st-half 2024-08-09 18:34:18 2024-08-09 18:01:37
## 6 19172016 1st-half 2024-08-09 18:35:27 2024-08-09 18:01:37
## # ℹ 109 more variables: match_start_datetime <dttm>, minute <int>,
## # second <int>, latest_bookmaker_update <chr>, suspended <chr>,
## # stopped <chr>, X1 <dbl>, X2 <dbl>, X <dbl>, name <chr>, ticking <chr>,
## # Accurate.Crosses...away <dbl>, Accurate.Crosses...home <dbl>,
## # Assists...away <dbl>, Assists...home <dbl>, Attacks...away <dbl>,
## # Attacks...home <dbl>, Ball.Possession.....away <dbl>,
## # Ball.Possession.....home <dbl>, Ball.Safe...away <dbl>, …colSums(is.na(match_data_filled))## fixture_id halftime
## 0 0
## current_time half_start_datetime
## 0 0
## match_start_datetime minute
## 0 0
## second latest_bookmaker_update
## 0 0
## suspended stopped
## 0 0
## X1 X2
## 0 0
## X name
## 0 0
## ticking Accurate.Crosses...away
## 0 0
## Accurate.Crosses...home Assists...away
## 0 0
## Assists...home Attacks...away
## 0 0
## Attacks...home Ball.Possession.....away
## 0 0
## Ball.Possession.....home Ball.Safe...away
## 0 0
## Ball.Safe...home Challenges...away
## 0 0
## Challenges...home Corners...away
## 0 0
## Corners...home Counter.Attacks...away
## 0 0
## Counter.Attacks...home Dangerous.Attacks...away
## 0 0
## Dangerous.Attacks...home Dribble.Attempts...away
## 0 0
## Dribble.Attempts...home Fouls...away
## 0 0
## Fouls...home Free.Kicks...away
## 0 0
## Free.Kicks...home Goal.Attempts...away
## 0 0
## Goal.Attempts...home Goal.Kicks...away
## 0 0
## Goal.Kicks...home Goals...away
## 0 0
## Goals...home Headers...away
## 0 0
## Headers...home Hit.Woodwork...away
## 0 0
## Hit.Woodwork...home Injuries...away
## 0 0
## Injuries...home Interceptions...away
## 0 0
## Interceptions...home Key.Passes...away
## 0 0
## Key.Passes...home Long.Passes...away
## 0 0
## Long.Passes...home Offsides...away
## 0 0
## Offsides...home Passes...away
## 0 0
## Passes...home Penalties...away
## 0 0
## Penalties...home Redcards...away
## 0 0
## Redcards...home Saves...away
## 0 0
## Saves...home Score.Change...away
## 0 0
## Score.Change...home Shots.Blocked...away
## 0 0
## Shots.Blocked...home Shots.Insidebox...away
## 0 0
## Shots.Insidebox...home Shots.Off.Target...away
## 0 0
## Shots.Off.Target...home Shots.On.Target...away
## 0 0
## Shots.On.Target...home Shots.Outsidebox...away
## 0 0
## Shots.Outsidebox...home Shots.Total...away
## 0 0
## Shots.Total...home Substitutions...away
## 0 0
## Substitutions...home Successful.Dribbles...away
## 0 0
## Successful.Dribbles...home Successful.Headers...away
## 0 0
## Successful.Headers...home Successful.Interceptions...away
## 0 0
## Successful.Interceptions...home Successful.Passes...away
## 0 0
## Successful.Passes...home Successful.Passes.Percentage...away
## 0 0
## Successful.Passes.Percentage...home Tackles...away
## 0 0
## Tackles...home Throwins...away
## 0 0
## Throwins...home Total.Crosses...away
## 0 0
## Total.Crosses...home Yellowcards...away
## 0 0
## Yellowcards...home Yellowred.Cards...away
## 0 0
## Yellowred.Cards...home current_state
## 0 0
## final_score result
## 0 0
## P_home P_draw
## 0 0
## P_away total_prob
## 0 0
## P_home_norm P_draw_norm
## 0 0
## P_away_norm
## 0match_data_filled <- match_data_filled %>%
mutate(
total_minute = case_when(
halftime == "1st-half" ~ minute,
halftime == "2nd-half" ~ 45 + minute
)
)
match_data_filled$result <- as.factor(match_data_filled$result)## Interaction terms
match_data_featured <- match_data_filled %>%
mutate(
goal_difference = `Goals...home` - `Goals...away`,
yellow_card_difference = `Yellowcards...home` - `Yellowcards...away`,
# Goal Impact
goal_elapsed_interaction = goal_difference * total_minute,
goal_yellowcards_home_interaction = goal_difference * `Yellowcards...home`,
goal_yellowcards_away_interaction = goal_difference * `Yellowcards...away`,
# Attack Efficiency
attack_efficiency_home = `Total.Crosses...home` * `Goals...home`,
interaction_passes_attacks_home = Passes...home * Attacks...home,
interaction_passes_attacks_away = Passes...away * Attacks...away,
attack_efficiency_away = `Total.Crosses...away` * `Goals...away`
)match_data_featured$halftime <- ifelse(match_data_featured$halftime == "1st-half", 1,
ifelse(match_data_featured$halftime == "2nd-half", 2, NA))
match_data_featured$current_state <- ifelse(match_data_featured$current_state == "X" | match_data_featured$current_state == "",
0,
match_data_featured$current_state)
match_data_featured$result <- ifelse(match_data_featured$result == "X", 0, match_data_featured$result)
match_data_featured$current_state <- as.numeric(match_data_featured$current_state)
match_data_featured$result <- as.factor(match_data_featured$result)initial_training_data <- match_data_featured %>% filter(match_start_datetime < "2024-11-01")
initial_test_data <- match_data_featured %>% filter(match_start_datetime >= "2024-11-01")unnecessary_cols <- c(
"fixture_id", "half_start_datetime", "match_start_datetime",
"latest_bookmaker_update", "name",
"current_time", "minute", "second", "suspended", "stopped",
"ticking", "final_score", "Score.Change...away",
"Score.Change...home", "P_home","P_away","P_draw"
)cleaned_training_data <- initial_training_data[, !(names(initial_training_data) %in% unnecessary_cols)]
cleaned_test_data <- initial_test_data[, !(names(initial_test_data) %in% unnecessary_cols)]library(corrplot)## corrplot 0.95 loadednumeric_columns <- names(cleaned_training_data)[names(cleaned_training_data) != "result"]
cor_matrix <- cor(cleaned_training_data[, numeric_columns], use = "complete.obs")
cor_pairs <- as.data.frame(as.table(cor_matrix))
cor_pairs <- cor_pairs[cor_pairs$Var1 != cor_pairs$Var2, ]
cor_pairs <- cor_pairs[order(-abs(cor_pairs$Freq)), ]
top_30_pairs <- head(cor_pairs, 30)
print(top_30_pairs)## Var1 Var2
## 1617 Interceptions...home Challenges...home
## 4321 Challenges...home Interceptions...home
## 1511 Interceptions...away Challenges...away
## 4215 Challenges...away Interceptions...away
## 1062 Ball.Possession.....home Ball.Possession.....away
## 1166 Ball.Possession.....away Ball.Possession.....home
## 5223 Successful.Passes...home Passes...home
## 8135 Passes...home Successful.Passes...home
## 5117 Successful.Passes...away Passes...away
## 8029 Passes...away Successful.Passes...away
## 3749 Successful.Headers...home Headers...home
## 7701 Headers...home Successful.Headers...home
## 3643 Successful.Headers...away Headers...away
## 7595 Headers...away Successful.Headers...away
## 4583 Shots.Total...home Key.Passes...home
## 7079 Key.Passes...home Shots.Total...home
## 1274 Ball.Safe...home Ball.Safe...away
## 1378 Ball.Safe...away Ball.Safe...home
## 4477 Shots.Total...away Key.Passes...away
## 6973 Key.Passes...away Shots.Total...away
## 10179 goal_elapsed_interaction goal_difference
## 10387 goal_difference goal_elapsed_interaction
## 5248 interaction_passes_attacks_home Passes...home
## 10760 Passes...home interaction_passes_attacks_home
## 8188 interaction_passes_attacks_home Successful.Passes...home
## 10788 Successful.Passes...home interaction_passes_attacks_home
## 5144 interaction_passes_attacks_away Passes...away
## 10864 Passes...away interaction_passes_attacks_away
## 995 Passes...home Attacks...home
## 5155 Attacks...home Passes...home
## Freq
## 1617 0.9962334
## 4321 0.9962334
## 1511 0.9954888
## 4215 0.9954888
## 1062 -0.9943634
## 1166 -0.9943634
## 5223 0.9940576
## 8135 0.9940576
## 5117 0.9932703
## 8029 0.9932703
## 3749 0.9640092
## 7701 0.9640092
## 3643 0.9612948
## 7595 0.9612948
## 4583 0.9590936
## 7079 0.9590936
## 1274 0.9559889
## 1378 0.9559889
## 4477 0.9485418
## 6973 0.9485418
## 10179 0.9364413
## 10387 0.9364413
## 5248 0.9322859
## 10760 0.9322859
## 8188 0.9308304
## 10788 0.9308304
## 5144 0.9291687
## 10864 0.9291687
## 995 0.9289726
## 5155 0.9289726str(cleaned_training_data)## tibble [46,291 × 106] (S3: tbl_df/tbl/data.frame)
## $ halftime : num [1:46291] 1 1 1 1 1 1 1 1 1 1 ...
## $ X1 : num [1:46291] 1.22 1.2 1.2 1.2 1.2 1.22 1.22 1.22 1.25 1.25 ...
## $ X2 : num [1:46291] 10 13 13 13 15 13 13 13 13 13 ...
## $ X : num [1:46291] 6.5 6 6 6 6 5.5 5.5 5.5 5.5 5 ...
## $ Accurate.Crosses...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Accurate.Crosses...home : num [1:46291] 0 1 1 1 1 1 1 1 1 1 ...
## $ Assists...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Assists...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Attacks...away : num [1:46291] 2 12 12 12 15 19 20 23 23 24 ...
## $ Attacks...home : num [1:46291] 18 40 40 42 46 48 48 51 51 51 ...
## $ Ball.Possession.....away : num [1:46291] 28 24 21 22 21 23 23 26 26 26 ...
## $ Ball.Possession.....home : num [1:46291] 72 76 79 78 79 77 77 74 74 74 ...
## $ Ball.Safe...away : num [1:46291] 9 9 9 9 9 9 9 9 9 9 ...
## $ Ball.Safe...home : num [1:46291] 7 7 7 7 7 7 7 7 7 7 ...
## $ Challenges...away : num [1:46291] 1 2 2 2 2 3 3 3 3 3 ...
## $ Challenges...home : num [1:46291] 1 2 2 2 3 3 3 3 3 3 ...
## $ Corners...away : num [1:46291] 0 1 1 1 1 1 1 1 1 1 ...
## $ Corners...home : num [1:46291] 0 4 4 4 5 5 5 5 5 5 ...
## $ Counter.Attacks...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Counter.Attacks...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Dangerous.Attacks...away : num [1:46291] 0 5 5 5 5 6 6 8 8 8 ...
## $ Dangerous.Attacks...home : num [1:46291] 9 29 29 32 36 37 37 37 37 37 ...
## $ Dribble.Attempts...away : num [1:46291] 1 3 3 3 3 4 4 5 5 5 ...
## $ Dribble.Attempts...home : num [1:46291] 3 5 6 6 6 6 6 6 6 6 ...
## $ Fouls...away : num [1:46291] 1 1 2 2 3 3 3 4 4 4 ...
## $ Fouls...home : num [1:46291] 1 1 1 1 1 1 1 1 1 1 ...
## $ Free.Kicks...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Free.Kicks...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Goal.Attempts...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Goal.Attempts...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Goal.Kicks...away : num [1:46291] 1 1 1 1 1 1 1 1 1 1 ...
## $ Goal.Kicks...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Goals...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Goals...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Headers...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Headers...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Hit.Woodwork...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Hit.Woodwork...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Injuries...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Injuries...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Interceptions...away : num [1:46291] 1 2 2 2 2 3 3 3 3 3 ...
## $ Interceptions...home : num [1:46291] 1 2 2 3 3 3 3 3 3 3 ...
## $ Key.Passes...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Key.Passes...home : num [1:46291] 0 2 2 2 3 3 3 4 4 4 ...
## $ Long.Passes...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Long.Passes...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Offsides...away : num [1:46291] 1 1 1 1 1 1 1 1 1 1 ...
## $ Offsides...home : num [1:46291] 1 1 1 1 1 1 1 1 1 1 ...
## $ Passes...away : num [1:46291] 24 38 40 45 45 54 54 67 67 67 ...
## $ Passes...home : num [1:46291] 60 116 145 153 158 174 174 183 183 183 ...
## $ Penalties...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Penalties...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Redcards...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Redcards...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Saves...away : num [1:46291] 1 2 2 2 2 2 2 2 2 2 ...
## $ Saves...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Shots.Blocked...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Shots.Blocked...home : num [1:46291] 0 3 3 3 4 4 4 4 4 4 ...
## $ Shots.Insidebox...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Shots.Insidebox...home : num [1:46291] 1 3 3 3 4 4 4 5 5 5 ...
## $ Shots.Off.Target...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Shots.Off.Target...home : num [1:46291] 0 0 0 0 0 1 1 1 1 1 ...
## $ Shots.On.Target...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Shots.On.Target...home : num [1:46291] 1 2 2 2 2 2 2 2 2 2 ...
## $ Shots.Outsidebox...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Shots.Outsidebox...home : num [1:46291] 0 2 2 2 2 2 2 2 2 2 ...
## $ Shots.Total...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Shots.Total...home : num [1:46291] 1 5 5 5 6 7 7 7 7 7 ...
## $ Substitutions...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Substitutions...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Successful.Dribbles...away : num [1:46291] 0 1 1 1 1 2 2 2 2 2 ...
## $ Successful.Dribbles...home : num [1:46291] 2 3 3 3 3 3 3 3 3 3 ...
## $ Successful.Headers...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Successful.Headers...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Successful.Interceptions...away : num [1:46291] 1 2 2 2 2 3 3 3 3 3 ...
## $ Successful.Interceptions...home : num [1:46291] 1 2 2 2 3 3 3 3 3 3 ...
## $ Successful.Passes...away : num [1:46291] 14 20 20 25 25 30 30 43 43 43 ...
## $ Successful.Passes...home : num [1:46291] 55 101 128 134 138 150 150 156 156 156 ...
## $ Successful.Passes.Percentage...away: num [1:46291] 58 52 50 55 55 55 55 64 64 64 ...
## $ Successful.Passes.Percentage...home: num [1:46291] 91 87 88 87 87 86 86 85 85 85 ...
## $ Tackles...away : num [1:46291] 3 8 10 11 11 11 11 11 11 11 ...
## $ Tackles...home : num [1:46291] 1 5 5 5 5 6 6 7 7 7 ...
## $ Throwins...away : num [1:46291] 3 6 6 6 7 8 8 9 9 12 ...
## $ Throwins...home : num [1:46291] 1 11 11 11 11 11 11 12 12 12 ...
## $ Total.Crosses...away : num [1:46291] 0 1 1 1 1 1 1 1 1 1 ...
## $ Total.Crosses...home : num [1:46291] 3 12 13 13 14 15 15 15 15 15 ...
## $ Yellowcards...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Yellowcards...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Yellowred.Cards...away : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ Yellowred.Cards...home : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ current_state : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ result : Factor w/ 3 levels "0","1","2": 2 2 2 2 2 2 2 2 2 2 ...
## $ total_prob : num [1:46291] 1.07 1.08 1.08 1.08 1.07 ...
## $ P_home_norm : num [1:46291] 0.764 0.774 0.774 0.774 0.781 ...
## $ P_draw_norm : num [1:46291] 0.143 0.155 0.155 0.155 0.156 ...
## $ P_away_norm : num [1:46291] 0.0932 0.0714 0.0714 0.0714 0.0625 ...
## $ total_minute : num [1:46291] 9 25 26 27 32 33 34 35 36 37 ...
## $ goal_difference : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## $ yellow_card_difference : num [1:46291] 0 0 0 0 0 0 0 0 0 0 ...
## [list output truncated]any(is.na(cleaned_training_data))## [1] FALSEfeature_scores <- information_gain(result ~ ., data = cleaned_training_data)str(feature_scores)## 'data.frame': 105 obs. of 2 variables:
## $ attributes: chr "halftime" "X1" "X2" "X" ...
## $ importance: num 0.000508 0.267573 0.265252 0.079766 0.005685 ...feature_scores$importance <- as.numeric(feature_scores$importance)
selected_features <- rownames(feature_scores)[feature_scores$importance > mean(feature_scores$importance, na.rm = TRUE)]
print(selected_features)## [1] "2" "3" "4" "7" "8" "14" "33" "34" "91" "93" "94" "95"
## [13] "97" "99" "100" "101" "102" "105"dt_model <- rpart(result ~ ., data = cleaned_training_data, method = "class",control = rpart.control(cp = 0.001, minsplit = 10, maxdepth = 15))rpart.plot(dt_model)## Warning: labs do not fit even at cex 0.15, there may be some overplotting
variable_importance <- dt_model$variable.importance
print(variable_importance)## P_home_norm X1
## 7551.37235 7472.01045
## P_away_norm X2
## 6795.72634 6734.35095
## goal_elapsed_interaction P_draw_norm
## 3455.51946 3451.38183
## X goal_difference
## 3357.34005 3317.64162
## total_minute Ball.Possession.....away
## 605.66817 495.87930
## Challenges...home Ball.Possession.....home
## 476.38340 459.77945
## Successful.Passes.Percentage...away Interceptions...home
## 456.42079 447.90488
## interaction_passes_attacks_home Ball.Safe...home
## 391.38961 390.01212
## Ball.Safe...away Attacks...away
## 367.25274 334.06951
## interaction_passes_attacks_away Headers...home
## 326.75474 323.22808
## Shots.Total...home Key.Passes...home
## 313.01921 312.54335
## Successful.Dribbles...home Successful.Passes...away
## 299.44331 296.13321
## Interceptions...away Successful.Passes.Percentage...home
## 270.44835 267.62988
## Passes...away Shots.Total...away
## 263.35036 254.79469
## Successful.Headers...away Challenges...away
## 254.37480 252.28769
## Accurate.Crosses...home Long.Passes...home
## 244.74939 236.59001
## Tackles...away Dribble.Attempts...home
## 231.35958 230.27255
## Tackles...home Shots.Insidebox...home
## 229.70487 228.27723
## Passes...home Successful.Interceptions...away
## 208.81438 205.20666
## Dangerous.Attacks...away Dangerous.Attacks...home
## 201.16883 198.39917
## yellow_card_difference Goal.Attempts...away
## 195.12074 193.69565
## Offsides...home Headers...away
## 190.59646 184.70309
## Key.Passes...away Counter.Attacks...home
## 178.17195 170.79567
## Free.Kicks...away Attacks...home
## 170.49331 168.81240
## Substitutions...away Goal.Attempts...home
## 167.85467 166.92487
## Total.Crosses...away Dribble.Attempts...away
## 166.63901 164.86942
## Total.Crosses...home Successful.Headers...home
## 164.21965 163.98423
## Goal.Kicks...home Long.Passes...away
## 161.03572 157.64508
## Accurate.Crosses...away Successful.Passes...home
## 154.19768 152.36031
## Successful.Interceptions...home Hit.Woodwork...home
## 145.26350 141.69706
## Shots.Off.Target...home Corners...home
## 141.49131 137.57256
## Fouls...home Assists...home
## 137.30568 128.43944
## Shots.Insidebox...away Saves...home
## 126.94173 122.02400
## Shots.Off.Target...away Shots.Outsidebox...home
## 121.98441 120.66274
## Fouls...away Shots.Outsidebox...away
## 119.30040 118.82073
## Throwins...away Free.Kicks...home
## 117.12047 113.27217
## Yellowcards...home Yellowcards...away
## 110.71691 108.39094
## Throwins...home Counter.Attacks...away
## 107.82374 105.75749
## Shots.On.Target...home Shots.On.Target...away
## 105.10543 97.81753
## attack_efficiency_home Shots.Blocked...home
## 90.88259 82.62059
## current_state Successful.Dribbles...away
## 80.13592 79.81852
## Saves...away goal_yellowcards_home_interaction
## 78.23198 75.45597
## attack_efficiency_away Goal.Kicks...away
## 65.52038 65.39587
## Shots.Blocked...away Corners...away
## 62.85152 59.61846
## Penalties...home goal_yellowcards_away_interaction
## 54.60509 49.38260
## Penalties...away Offsides...away
## 46.52758 44.84274
## Goals...away Redcards...home
## 38.62082 35.67122
## Injuries...away Injuries...home
## 27.66863 23.30927
## Assists...away Redcards...away
## 19.30335 14.18599
## Goals...home Hit.Woodwork...away
## 13.36234 1.84820As can be seen from these results, adding the interaction terms goal_yellowcards_away_interaction attack_efficiency_away oal_yellowcards_home_interaction yellow_card_difference to the model does not leave room for improvement in the model and increases the risk of overfitting.
importance_df <- data.frame(
Feature = names(variable_importance),
Importance = variable_importance
)
top_10_importance_df <- importance_df[1:10, ]
ggplot(top_10_importance_df, aes(x = reorder(Feature, Importance), y = Importance)) +
geom_bar(stat = "identity") +
coord_flip() +
labs(title = "Top 10 Feature Importance", x = "Features", y = "Importance") +
theme_minimal()
tree_model_predictions <- predict(dt_model, newdata = initial_test_data, type = "class")
conf_matrix <- confusionMatrix(tree_model_predictions, initial_test_data$result)
print(conf_matrix)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 935 1220 504
## 1 566 2967 419
## 2 718 697 1810
##
## Overall Statistics
##
## Accuracy : 0.5807
## 95% CI : (0.5709, 0.5905)
## No Information Rate : 0.4965
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.3534
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.42136 0.6075 0.6623
## Specificity 0.77366 0.8011 0.8008
## Pos Pred Value 0.35164 0.7508 0.5612
## Neg Pred Value 0.82110 0.6742 0.8604
## Prevalence 0.22560 0.4965 0.2779
## Detection Rate 0.09506 0.3016 0.1840
## Detection Prevalence 0.27033 0.4018 0.3279
## Balanced Accuracy 0.59751 0.7043 0.7315unnecessary_cols2 <- c(
"half_start_datetime", "match_start_datetime",
"latest_bookmaker_update", "name",
"current_time", "minute", "second", "suspended", "stopped",
"ticking", "final_score", "Score.Change...away",
"Score.Change...home"
)cleaned_data <- match_data_featured[, !(names(match_data_featured) %in% unnecessary_cols2)]
first_minutes <- cleaned_data %>%
group_by(fixture_id) %>%
slice(1) %>%
ungroup()
# P_home_norm ile P_away_norm arasındaki farkı hesaplama
first_minutes <- first_minutes %>%
mutate(home_away_diff = P_home_norm - P_away_norm)# Calculate the 33.33rd and 66.67th percentiles
thresholds <- quantile(first_minutes$home_away_diff, probs = c(0.3333, 0.6667))
print(thresholds)## 33.33% 66.67%
## -0.00276873 0.30227374first_minutes <- first_minutes[order(abs(first_minutes$home_away_diff)), ]
n <- nrow(first_minutes)
group_size <- ceiling(n / 3)
# Create a new column to assign groups
first_minutes$category <- c(
rep("Good", group_size),
rep("Medium", group_size),
rep("Bad", n - 2 * group_size) # Remaining entries go to the last group
)
# Display the updated table
print(first_minutes)## # A tibble: 648 × 112
## fixture_id halftime X1 X2 X Accurate.Crosses...away
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 19134876 1 2.62 2.62 3.25 0
## 2 19135286 1 2.75 2.75 3 0
## 3 19135312 1 3 3 2.55 0
## 4 19135333 1 2.87 2.87 2.8 0
## 5 19135337 1 2.7 2.7 3.2 0
## 6 19135343 1 2.62 2.62 3.25 0
## 7 19155168 1 2.75 2.75 3 0
## 8 19172017 1 2.62 2.62 3.25 0
## 9 19172101 1 2.62 2.62 3.25 0
## 10 19139713 1 2.62 2.6 3.25 0
## # ℹ 638 more rows
## # ℹ 106 more variables: Accurate.Crosses...home <dbl>, Assists...away <dbl>,
## # Assists...home <dbl>, Attacks...away <dbl>, Attacks...home <dbl>,
## # Ball.Possession.....away <dbl>, Ball.Possession.....home <dbl>,
## # Ball.Safe...away <dbl>, Ball.Safe...home <dbl>, Challenges...away <dbl>,
## # Challenges...home <dbl>, Corners...away <dbl>, Corners...home <dbl>,
## # Counter.Attacks...away <dbl>, Counter.Attacks...home <dbl>, …lookup_table <- first_minutes[, c("fixture_id", "category")]
colnames(lookup_table) <- c("fixture_id", "category")
cleaned_data <- merge(cleaned_data, lookup_table, by = "fixture_id", all.x = TRUE)
cleaned_data <- cleaned_data %>%
mutate(home_away_diff = abs(P_home_norm - P_away_norm))
print(cleaned_data)## fixture_id halftime X1 X2 X Accurate.Crosses...away
## 1 19134453 1 1.66 5.00 4.00 0
## 2 19134453 1 1.66 5.00 4.00 0
## 3 19134453 1 1.61 5.50 4.00 0
## 4 19134453 1 1.61 5.00 4.00 0
## 5 19134453 1 1.61 5.00 4.00 0
## 6 19134453 1 1.61 5.00 4.00 0
## 7 19134453 1 1.61 5.50 4.00 0
## 8 19134453 1 1.61 5.00 4.00 0
## 9 19134453 1 1.61 5.00 3.75 0
## 10 19134453 1 1.66 4.75 3.75 0
## 11 19134453 1 1.66 5.00 3.75 0
## 12 19134453 1 1.61 5.50 3.75 0
## 13 19134453 1 1.61 5.50 3.75 0
## 14 19134453 1 1.61 5.50 3.75 0
## 15 19134453 1 1.57 5.50 4.00 1
## 16 19134453 1 1.61 5.50 3.75 1
## 17 19134453 1 1.61 5.50 3.75 1
## 18 19134453 1 1.61 5.50 3.75 1
## 19 19134453 1 1.66 5.50 3.75 1
## 20 19134453 1 1.66 5.50 3.75 1
## 21 19134453 1 1.66 5.50 3.75 1
## 22 19134453 1 1.66 5.50 3.60 1
## 23 19134453 1 1.66 5.50 3.60 1
## 24 19134453 1 1.66 5.50 3.60 1
## 25 19134453 1 1.66 5.50 3.60 1
## 26 19134453 1 1.66 5.50 3.60 1
## 27 19134453 1 1.66 5.50 3.50 1
## 28 19134453 1 1.66 6.00 3.50 1
## 29 19134453 1 1.66 6.00 3.50 1
## 30 19134453 1 1.61 6.50 3.50 1
## 31 19134453 1 1.61 6.50 3.50 1
## 32 19134453 1 1.61 6.50 3.50 1
## 33 19134453 1 1.61 6.50 3.50 1
## 34 19134453 1 1.61 6.50 3.40 1
## 35 19134453 1 1.61 6.50 3.40 1
## 36 19134453 1 1.61 6.50 3.40 1
## 37 19134453 1 1.61 6.50 3.40 1
## 38 19134453 1 1.61 6.50 3.40 1
## 39 19134453 1 1.61 7.00 3.40 1
## 40 19134453 1 1.61 7.00 3.40 1
## 41 19134453 1 1.66 6.50 3.25 1
## 42 19134453 1 1.66 6.50 3.20 1
## 43 19134453 1 1.66 6.50 3.20 1
## 44 19134453 1 1.66 6.50 3.10 1
## 45 19134453 1 1.66 7.00 3.10 1
## 46 19134453 1 1.66 7.00 3.10 1
## 47 19134453 2 1.72 6.50 3.00 1
## 48 19134453 2 1.80 6.00 2.87 1
## 49 19134453 2 1.80 6.00 2.87 2
## 50 19134453 2 1.83 6.00 2.75 2
## 51 19134453 2 1.90 6.00 2.75 3
## 52 19134453 2 1.95 5.50 2.75 3
## 53 19134453 2 2.00 5.50 2.62 3
## 54 19134453 2 1.95 5.50 2.62 3
## 55 19134453 2 2.00 5.50 2.60 3
## 56 19134453 2 1.95 6.00 2.60 3
## 57 19134453 2 1.95 6.00 2.50 3
## 58 19134453 2 1.95 6.50 2.50 3
## 59 19134453 2 1.95 6.50 2.50 3
## 60 19134453 2 2.00 6.50 2.40 3
## 61 19134453 2 2.00 7.00 2.40 3
## 62 19134453 2 2.00 7.00 2.40 3
## 63 19134453 2 2.05 7.00 2.37 3
## 64 19134453 2 2.10 7.50 2.25 3
## 65 19134453 2 2.10 6.50 2.30 3
## 66 19134453 2 2.20 7.00 2.20 3
## 67 19134453 2 2.10 7.00 2.20 3
## 68 19134453 2 2.20 7.00 2.20 3
## 69 19134453 2 2.25 7.00 2.10 3
## 70 19134453 2 2.30 7.00 2.10 3
## 71 19134453 2 2.37 7.00 2.05 3
## 72 19134453 2 2.40 7.00 1.95 3
## 73 19134453 2 2.50 6.50 2.00 3
## 74 19134453 2 2.50 6.50 1.95 3
## 75 19134453 2 2.60 6.50 1.90 3
## 76 19134453 2 2.75 6.50 1.80 3
## 77 19134453 2 2.87 7.00 1.80 4
## 78 19134453 2 2.87 7.00 1.72 5
## 79 19134453 2 3.00 7.00 1.72 5
## 80 19134453 2 3.10 7.00 1.66 5
## 81 19134453 2 3.20 7.50 1.61 5
## 82 19134453 2 3.40 7.50 1.57 5
## 83 19134453 2 3.50 7.50 1.57 5
## 84 19134453 2 3.60 8.50 1.50 5
## 85 19134453 2 3.75 9.00 1.44 5
## 86 19134453 2 4.33 8.50 1.40 5
## 87 19134453 2 4.75 10.00 1.33 5
## 88 19134453 2 1.07 101.00 9.00 5
## 89 19134453 2 1.06 151.00 10.00 5
## 90 19134453 2 1.09 81.00 7.50 5
## 91 19134453 2 1.04 301.00 13.00 5
## 92 19134453 2 1.02 451.00 17.00 5
## 93 19134453 2 1.01 501.00 21.00 5
## 94 19134453 2 1.00 501.00 26.00 6
## 95 19134454 1 8.00 1.33 5.50 0
## 96 19134454 1 8.00 1.33 5.50 0
## 97 19134454 1 8.00 1.33 5.50 0
## 98 19134454 1 7.50 1.33 5.50 0
## 99 19134454 1 7.50 1.33 5.50 0
## 100 19134454 1 7.50 1.33 5.50 0
## 101 19134454 1 7.50 1.33 5.50 0
## 102 19134454 1 7.50 1.36 5.50 0
## 103 19134454 1 7.50 1.33 5.50 0
## 104 19134454 1 7.50 1.33 5.50 0
## 105 19134454 1 8.00 1.36 5.00 0
## 106 19134454 1 7.50 1.36 5.00 0
## 107 19134454 1 7.50 1.36 5.00 0
## 108 19134454 1 7.50 1.40 4.75 0
## 109 19134454 1 7.50 1.40 5.00 0
## 110 19134454 1 7.00 1.40 4.75 0
## 111 19134454 1 7.00 1.40 4.75 0
## 112 19134454 1 7.00 1.40 4.75 0
## 113 19134454 1 7.00 1.40 4.75 0
## 114 19134454 1 6.50 1.44 4.50 0
## 115 19134454 1 7.00 1.44 4.50 0
## 116 19134454 1 7.00 1.44 4.50 0
## 117 19134454 1 7.00 1.44 4.33 0
## 118 19134454 1 7.00 1.44 4.33 0
## 119 19134454 1 7.00 1.44 4.33 0
## 120 19134454 1 7.50 1.44 4.33 0
## 121 19134454 1 7.50 1.44 4.33 0
## 122 19134454 1 8.00 1.44 4.33 0
## 123 19134454 1 7.50 1.44 4.33 0
## 124 19134454 1 7.50 1.44 4.00 0
## 125 19134454 1 7.50 1.44 4.00 0
## 126 19134454 1 7.50 1.44 4.00 0
## 127 19134454 1 7.50 1.44 4.00 0
## 128 19134454 1 7.50 1.50 4.00 0
## 129 19134454 1 7.50 1.50 4.00 0
## 130 19134454 1 7.50 1.50 3.75 0
## 131 19134454 1 7.50 1.50 3.75 0
## 132 19134454 1 7.50 1.50 3.75 0
## 133 19134454 1 7.50 1.53 3.60 0
## 134 19134454 1 7.50 1.53 3.60 0
## 135 19134454 1 7.50 1.53 3.60 0
## 136 19134454 1 7.00 1.57 3.50 0
## 137 19134454 1 6.50 1.61 3.40 0
## 138 19134454 1 6.50 1.61 3.40 0
## 139 19134454 1 6.50 1.66 3.25 0
## 140 19134454 1 6.50 1.66 3.25 0
## 141 19134454 2 7.50 1.57 3.40 0
## 142 19134454 2 7.50 1.57 3.40 0
## 143 19134454 2 7.50 1.57 3.40 0
## 144 19134454 2 7.50 1.61 3.25 0
## 145 19134454 2 8.00 1.57 3.25 0
## 146 19134454 2 8.00 1.61 3.20 0
## 147 19134454 2 7.50 1.61 3.20 0
## 148 19134454 2 7.50 1.66 3.10 1
## 149 19134454 2 8.00 1.66 3.00 1
## 150 19134454 2 7.50 1.66 3.10 1
## 151 19134454 2 7.50 1.66 3.10 1
## 152 19134454 2 8.00 1.66 3.00 2
## 153 19134454 2 34.00 1.10 8.00 2
## 154 19134454 2 41.00 1.09 8.50 2
## 155 19134454 2 41.00 1.08 8.50 2
## 156 19134454 2 41.00 1.08 8.50 2
## 157 19134454 2 41.00 1.08 8.50 2
## 158 19134454 2 101.00 1.00 26.00 2
## 159 19134454 2 101.00 1.00 26.00 2
## 160 19134454 2 101.00 1.00 26.00 2
## 161 19134454 2 101.00 1.00 26.00 2
## 162 19134454 2 101.00 1.00 26.00 3
## 163 19134454 2 101.00 1.00 26.00 3
## 164 19134454 2 101.00 1.00 26.00 3
## 165 19134454 2 101.00 1.00 29.00 3
## 166 19134454 2 101.00 1.00 29.00 3
## 167 19134454 2 101.00 1.00 29.00 3
## 168 19134454 2 101.00 1.00 29.00 3
## 169 19134454 2 251.00 1.00 41.00 3
## 170 19134454 2 251.00 1.00 41.00 3
## 171 19134454 2 251.00 1.00 41.00 4
## 172 19134454 2 301.00 1.00 41.00 4
## 173 19134454 2 301.00 1.00 41.00 4
## 174 19134454 2 301.00 1.00 41.00 4
## 175 19134454 2 301.00 1.00 41.00 4
## 176 19134454 2 301.00 1.00 41.00 4
## 177 19134454 2 351.00 1.00 41.00 4
## 178 19134454 2 401.00 1.00 51.00 4
## 179 19134454 2 401.00 1.00 51.00 4
## 180 19134454 2 401.00 1.00 51.00 4
## 181 19134454 2 451.00 1.00 51.00 4
## 182 19134455 1 1.14 15.00 8.00 0
## 183 19134455 1 1.16 13.00 8.00 0
## 184 19134455 1 1.16 13.00 7.50 0
## 185 19134455 1 1.18 13.00 7.50 0
## 186 19134455 1 1.18 12.00 7.00 0
## 187 19134455 1 1.18 12.00 7.00 0
## 188 19134455 1 1.18 12.00 7.00 0
## 189 19134455 1 1.20 12.00 7.00 0
## 190 19134455 1 1.20 12.00 6.50 0
## 191 19134455 1 1.20 12.00 6.50 0
## 192 19134455 1 1.22 12.00 6.50 0
## 193 19134455 1 1.22 11.00 6.50 0
## 194 19134455 1 1.22 11.00 6.50 0
## 195 19134455 1 1.22 11.00 6.50 0
## 196 19134455 1 1.22 12.00 6.50 0
## 197 19134455 1 1.22 12.00 6.50 0
## 198 19134455 1 1.22 12.00 6.50 0
## 199 19134455 1 1.22 12.00 6.50 0
## 200 19134455 1 1.20 13.00 6.50 0
## 201 19134455 1 1.20 13.00 6.50 0
## 202 19134455 1 1.20 13.00 6.50 0
## 203 19134455 1 1.20 13.00 6.50 0
## 204 19134455 1 1.20 13.00 6.50 0
## 205 19134455 1 1.20 13.00 6.50 0
## 206 19134455 1 1.05 29.00 13.00 0
## 207 19134455 1 1.05 29.00 13.00 0
## 208 19134455 1 1.06 26.00 12.00 0
## 209 19134455 1 1.05 29.00 13.00 0
## 210 19134455 1 1.05 29.00 12.00 0
## 211 19134455 1 1.05 29.00 12.00 0
## 212 19134455 1 1.05 29.00 12.00 0
## 213 19134455 1 1.05 29.00 12.00 0
## 214 19134455 1 1.06 29.00 11.00 0
## 215 19134455 1 1.06 29.00 11.00 0
## 216 19134455 1 1.06 29.00 11.00 1
## 217 19134455 1 1.06 29.00 11.00 1
## 218 19134455 1 1.06 29.00 11.00 1
## 219 19134455 1 1.06 29.00 11.00 1
## 220 19134455 1 1.06 29.00 11.00 1
## 221 19134455 1 1.06 29.00 11.00 1
## 222 19134455 1 1.07 29.00 11.00 1
## 223 19134455 1 1.07 29.00 11.00 1
## 224 19134455 1 1.07 29.00 10.00 1
## 225 19134455 1 1.07 34.00 10.00 1
## 226 19134455 1 1.07 34.00 10.00 1
## 227 19134455 2 1.05 34.00 11.00 1
## 228 19134455 2 1.05 34.00 11.00 1
## 229 19134455 2 1.05 41.00 11.00 1
## 230 19134455 2 1.05 41.00 11.00 1
## 231 19134455 2 1.05 41.00 11.00 1
## 232 19134455 2 1.06 41.00 11.00 1
## 233 19134455 2 1.06 41.00 10.00 1
## 234 19134455 2 1.06 41.00 10.00 1
## 235 19134455 2 1.06 41.00 10.00 1
## 236 19134455 2 1.06 41.00 10.00 1
## 237 19134455 2 1.06 41.00 10.00 1
## 238 19134455 2 1.06 41.00 10.00 1
## 239 19134455 2 1.06 41.00 10.00 1
## 240 19134455 2 1.06 41.00 10.00 1
## 241 19134455 2 1.06 41.00 10.00 1
## 242 19134455 2 1.06 41.00 10.00 1
## 243 19134455 2 1.06 41.00 9.50 1
## 244 19134455 2 1.06 41.00 9.50 2
## 245 19134455 2 1.06 41.00 9.50 2
## 246 19134455 2 1.06 51.00 10.00 2
## 247 19134455 2 1.06 51.00 9.50 2
## 248 19134455 2 1.06 51.00 9.50 2
## 249 19134455 2 1.06 51.00 10.00 2
## 250 19134455 2 1.06 51.00 10.00 2
## 251 19134455 2 1.06 51.00 10.00 2
## 252 19134455 2 1.00 301.00 41.00 2
## 253 19134455 2 1.00 301.00 41.00 2
## 254 19134455 2 1.00 301.00 41.00 2
## 255 19134455 2 1.00 301.00 41.00 2
## 256 19134455 2 1.00 301.00 41.00 2
## 257 19134455 2 1.00 301.00 41.00 2
## 258 19134455 2 1.00 351.00 41.00 2
## 259 19134455 2 1.00 351.00 41.00 2
## 260 19134455 2 1.00 351.00 41.00 2
## 261 19134455 2 1.00 401.00 41.00 2
## 262 19134455 2 1.00 401.00 51.00 2
## 263 19134455 2 1.00 451.00 51.00 2
## 264 19134456 1 3.10 2.30 3.40 0
## 265 19134456 1 3.10 2.30 3.40 0
## 266 19134456 1 3.00 2.30 3.40 0
## 267 19134456 1 3.00 2.30 3.40 0
## 268 19134456 1 3.00 2.37 3.40 0
## 269 19134456 1 2.87 2.37 3.40 0
## 270 19134456 1 2.87 2.40 3.25 0
## 271 19134456 1 2.87 2.40 3.25 0
## 272 19134456 1 2.87 2.50 3.25 0
## 273 19134456 1 2.87 2.50 3.25 0
## 274 19134456 1 2.87 2.50 3.25 0
## 275 19134456 1 2.87 2.50 3.25 0
## 276 19134456 1 2.87 2.50 3.25 0
## 277 19134456 1 2.75 2.50 3.20 0
## 278 19134456 1 2.75 2.60 3.20 1
## 279 19134456 1 2.75 2.60 3.20 1
## 280 19134456 1 2.75 2.60 3.20 1
## 281 19134456 1 2.75 2.60 3.20 1
## 282 19134456 1 2.75 2.60 3.10 1
## 283 19134456 1 2.75 2.60 3.10 1
## 284 19134456 1 2.75 2.62 3.10 1
## 285 19134456 1 2.75 2.62 3.10 1
## 286 19134456 1 2.75 2.62 3.10 1
## 287 19134456 1 2.75 2.75 3.10 1
## 288 19134456 1 2.75 2.75 3.10 1
## 289 19134456 1 6.00 1.53 4.00 1
## 290 19134456 1 6.50 1.53 4.00 1
## 291 19134456 1 6.50 1.53 4.00 1
## 292 19134456 1 6.50 1.53 4.00 1
## 293 19134456 1 6.50 1.53 4.00 1
## 294 19134456 1 6.50 1.53 4.00 1
## 295 19134456 1 6.50 1.53 4.00 1
## 296 19134456 1 6.50 1.53 4.00 1
## 297 19134456 1 6.50 1.53 4.00 1
## 298 19134456 1 6.50 1.53 3.75 1
## 299 19134456 1 6.50 1.53 3.75 1
## 300 19134456 1 7.00 1.53 3.75 1
## 301 19134456 1 6.50 1.53 3.75 1
## 302 19134456 1 7.00 1.53 3.75 1
## 303 19134456 1 7.00 1.50 3.75 1
## 304 19134456 1 7.50 1.50 3.75 1
## 305 19134456 1 7.50 1.50 3.75 1
## 306 19134456 1 7.50 1.50 3.75 1
## 307 19134456 1 7.50 1.50 3.75 1
## 308 19134456 1 7.50 1.50 3.75 1
## 309 19134456 2 8.50 1.44 4.00 1
## 310 19134456 2 3.75 2.30 2.75 1
## 311 19134456 2 10.00 1.40 4.00 1
## 312 19134456 2 10.00 1.40 4.00 1
## 313 19134456 2 10.00 1.40 4.00 1
## 314 19134456 2 11.00 1.36 4.00 1
## 315 19134456 2 11.00 1.36 4.00 1
## 316 19134456 2 11.00 1.36 4.00 1
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## current_state result P_home P_draw P_away total_prob
## 1 0 1 0.602409639 0.25000000 0.200000000 1.052410
## 2 0 1 0.602409639 0.25000000 0.200000000 1.052410
## 3 0 1 0.621118012 0.25000000 0.181818182 1.052936
## 4 0 1 0.621118012 0.25000000 0.200000000 1.071118
## 5 0 1 0.621118012 0.25000000 0.200000000 1.071118
## 6 0 1 0.621118012 0.25000000 0.200000000 1.071118
## 7 0 1 0.621118012 0.25000000 0.181818182 1.052936
## 8 0 1 0.621118012 0.25000000 0.200000000 1.071118
## 9 0 1 0.621118012 0.26666667 0.200000000 1.087785
## 10 0 1 0.602409639 0.26666667 0.210526316 1.079603
## 11 0 1 0.602409639 0.26666667 0.200000000 1.069076
## 12 0 1 0.621118012 0.26666667 0.181818182 1.069603
## 13 0 1 0.621118012 0.26666667 0.181818182 1.069603
## 14 0 1 0.621118012 0.26666667 0.181818182 1.069603
## 15 0 1 0.636942675 0.25000000 0.181818182 1.068761
## 16 0 1 0.621118012 0.26666667 0.181818182 1.069603
## 17 0 1 0.621118012 0.26666667 0.181818182 1.069603
## 18 0 1 0.621118012 0.26666667 0.181818182 1.069603
## 19 0 1 0.602409639 0.26666667 0.181818182 1.050894
## 20 0 1 0.602409639 0.26666667 0.181818182 1.050894
## 21 0 1 0.602409639 0.26666667 0.181818182 1.050894
## 22 0 1 0.602409639 0.27777778 0.181818182 1.062006
## 23 0 1 0.602409639 0.27777778 0.181818182 1.062006
## 24 0 1 0.602409639 0.27777778 0.181818182 1.062006
## 25 0 1 0.602409639 0.27777778 0.181818182 1.062006
## 26 0 1 0.602409639 0.27777778 0.181818182 1.062006
## 27 0 1 0.602409639 0.28571429 0.181818182 1.069942
## 28 0 1 0.602409639 0.28571429 0.166666667 1.054791
## 29 0 1 0.602409639 0.28571429 0.166666667 1.054791
## 30 0 1 0.621118012 0.28571429 0.153846154 1.060678
## 31 0 1 0.621118012 0.28571429 0.153846154 1.060678
## 32 0 1 0.621118012 0.28571429 0.153846154 1.060678
## 33 0 1 0.621118012 0.28571429 0.153846154 1.060678
## 34 0 1 0.621118012 0.29411765 0.153846154 1.069082
## 35 0 1 0.621118012 0.29411765 0.153846154 1.069082
## 36 0 1 0.621118012 0.29411765 0.153846154 1.069082
## 37 0 1 0.621118012 0.29411765 0.153846154 1.069082
## 38 0 1 0.621118012 0.29411765 0.153846154 1.069082
## 39 0 1 0.621118012 0.29411765 0.142857143 1.058093
## 40 0 1 0.621118012 0.29411765 0.142857143 1.058093
## 41 0 1 0.602409639 0.30769231 0.153846154 1.063948
## 42 0 1 0.602409639 0.31250000 0.153846154 1.068756
## 43 0 1 0.602409639 0.31250000 0.153846154 1.068756
## 44 0 1 0.602409639 0.32258065 0.153846154 1.078836
## 45 0 1 0.602409639 0.32258065 0.142857143 1.067847
## 46 0 1 0.602409639 0.32258065 0.142857143 1.067847
## 47 0 1 0.581395349 0.33333333 0.153846154 1.068575
## 48 0 1 0.555555556 0.34843206 0.166666667 1.070654
## 49 0 1 0.555555556 0.34843206 0.166666667 1.070654
## 50 0 1 0.546448087 0.36363636 0.166666667 1.076751
## 51 0 1 0.526315789 0.36363636 0.166666667 1.056619
## 52 0 1 0.512820513 0.36363636 0.181818182 1.058275
## 53 0 1 0.500000000 0.38167939 0.181818182 1.063498
## 54 0 1 0.512820513 0.38167939 0.181818182 1.076318
## 55 0 1 0.500000000 0.38461538 0.181818182 1.066434
## 56 0 1 0.512820513 0.38461538 0.166666667 1.064103
## 57 0 1 0.512820513 0.40000000 0.166666667 1.079487
## 58 0 1 0.512820513 0.40000000 0.153846154 1.066667
## 59 0 1 0.512820513 0.40000000 0.153846154 1.066667
## 60 0 1 0.500000000 0.41666667 0.153846154 1.070513
## 61 0 1 0.500000000 0.41666667 0.142857143 1.059524
## 62 0 1 0.500000000 0.41666667 0.142857143 1.059524
## 63 0 1 0.487804878 0.42194093 0.142857143 1.052603
## 64 0 1 0.476190476 0.44444444 0.133333333 1.053968
## 65 0 1 0.476190476 0.43478261 0.153846154 1.064819
## 66 0 1 0.454545455 0.45454545 0.142857143 1.051948
## 67 0 1 0.476190476 0.45454545 0.142857143 1.073593
## 68 0 1 0.454545455 0.45454545 0.142857143 1.051948
## 69 0 1 0.444444444 0.47619048 0.142857143 1.063492
## 70 0 1 0.434782609 0.47619048 0.142857143 1.053830
## 71 0 1 0.421940928 0.48780488 0.142857143 1.052603
## 72 0 1 0.416666667 0.51282051 0.142857143 1.072344
## 73 0 1 0.400000000 0.50000000 0.153846154 1.053846
## 74 0 1 0.400000000 0.51282051 0.153846154 1.066667
## 75 0 1 0.384615385 0.52631579 0.153846154 1.064777
## 76 0 1 0.363636364 0.55555556 0.153846154 1.073038
## 77 0 1 0.348432056 0.55555556 0.142857143 1.046845
## 78 0 1 0.348432056 0.58139535 0.142857143 1.072685
## 79 0 1 0.333333333 0.58139535 0.142857143 1.057586
## 80 0 1 0.322580645 0.60240964 0.142857143 1.067847
## 81 0 1 0.312500000 0.62111801 0.133333333 1.066951
## 82 0 1 0.294117647 0.63694268 0.133333333 1.064394
## 83 0 1 0.285714286 0.63694268 0.133333333 1.055990
## 84 0 1 0.277777778 0.66666667 0.117647059 1.062092
## 85 0 1 0.266666667 0.69444444 0.111111111 1.072222
## 86 0 1 0.230946882 0.71428571 0.117647059 1.062880
## 87 0 1 0.210526316 0.75187970 0.100000000 1.062406
## 88 1 1 0.934579439 0.11111111 0.009900990 1.055592
## 89 1 1 0.943396226 0.10000000 0.006622517 1.050019
## 90 1 1 0.917431193 0.13333333 0.012345679 1.063110
## 91 1 1 0.961538462 0.07692308 0.003322259 1.041784
## 92 1 1 0.980392157 0.05882353 0.002217295 1.041433
## 93 1 1 0.990099010 0.04761905 0.001996008 1.039714
## 94 1 1 1.000000000 0.03846154 0.001996008 1.040458
## 95 0 2 0.125000000 0.18181818 0.751879699 1.058698
## 96 0 2 0.125000000 0.18181818 0.751879699 1.058698
## 97 0 2 0.125000000 0.18181818 0.751879699 1.058698
## 98 0 2 0.133333333 0.18181818 0.751879699 1.067031
## 99 0 2 0.133333333 0.18181818 0.751879699 1.067031
## 100 0 2 0.133333333 0.18181818 0.751879699 1.067031
## 101 0 2 0.133333333 0.18181818 0.751879699 1.067031
## 102 0 2 0.133333333 0.18181818 0.735294118 1.050446
## 103 0 2 0.133333333 0.18181818 0.751879699 1.067031
## 104 0 2 0.133333333 0.18181818 0.751879699 1.067031
## 105 0 2 0.125000000 0.20000000 0.735294118 1.060294
## 106 0 2 0.133333333 0.20000000 0.735294118 1.068627
## 107 0 2 0.133333333 0.20000000 0.735294118 1.068627
## 108 0 2 0.133333333 0.21052632 0.714285714 1.058145
## 109 0 2 0.133333333 0.20000000 0.714285714 1.047619
## 110 0 2 0.142857143 0.21052632 0.714285714 1.067669
## 111 0 2 0.142857143 0.21052632 0.714285714 1.067669
## 112 0 2 0.142857143 0.21052632 0.714285714 1.067669
## 113 0 2 0.142857143 0.21052632 0.714285714 1.067669
## 114 0 2 0.153846154 0.22222222 0.694444444 1.070513
## 115 0 2 0.142857143 0.22222222 0.694444444 1.059524
## 116 0 2 0.142857143 0.22222222 0.694444444 1.059524
## 117 0 2 0.142857143 0.23094688 0.694444444 1.068248
## 118 0 2 0.142857143 0.23094688 0.694444444 1.068248
## 119 0 2 0.142857143 0.23094688 0.694444444 1.068248
## 120 0 2 0.133333333 0.23094688 0.694444444 1.058725
## 121 0 2 0.133333333 0.23094688 0.694444444 1.058725
## 122 0 2 0.125000000 0.23094688 0.694444444 1.050391
## 123 0 2 0.133333333 0.23094688 0.694444444 1.058725
## 124 0 2 0.133333333 0.25000000 0.694444444 1.077778
## 125 0 2 0.133333333 0.25000000 0.694444444 1.077778
## 126 0 2 0.133333333 0.25000000 0.694444444 1.077778
## 127 0 2 0.133333333 0.25000000 0.694444444 1.077778
## 128 0 2 0.133333333 0.25000000 0.666666667 1.050000
## 129 0 2 0.133333333 0.25000000 0.666666667 1.050000
## 130 0 2 0.133333333 0.26666667 0.666666667 1.066667
## 131 0 2 0.133333333 0.26666667 0.666666667 1.066667
## 132 0 2 0.133333333 0.26666667 0.666666667 1.066667
## 133 0 2 0.133333333 0.27777778 0.653594771 1.064706
## 134 0 2 0.133333333 0.27777778 0.653594771 1.064706
## 135 0 2 0.133333333 0.27777778 0.653594771 1.064706
## 136 0 2 0.142857143 0.28571429 0.636942675 1.065514
## 137 0 2 0.153846154 0.29411765 0.621118012 1.069082
## 138 0 2 0.153846154 0.29411765 0.621118012 1.069082
## 139 0 2 0.153846154 0.30769231 0.602409639 1.063948
## 140 0 2 0.153846154 0.30769231 0.602409639 1.063948
## 141 0 2 0.133333333 0.29411765 0.636942675 1.064394
## 142 0 2 0.133333333 0.29411765 0.636942675 1.064394
## 143 0 2 0.133333333 0.29411765 0.636942675 1.064394
## 144 0 2 0.133333333 0.30769231 0.621118012 1.062144
## 145 0 2 0.125000000 0.30769231 0.636942675 1.069635
## 146 0 2 0.125000000 0.31250000 0.621118012 1.058618
## 147 0 2 0.133333333 0.31250000 0.621118012 1.066951
## 148 0 2 0.133333333 0.32258065 0.602409639 1.058324
## 149 0 2 0.125000000 0.33333333 0.602409639 1.060743
## 150 0 2 0.133333333 0.32258065 0.602409639 1.058324
## 151 0 2 0.133333333 0.32258065 0.602409639 1.058324
## 152 0 2 0.125000000 0.33333333 0.602409639 1.060743
## 153 2 2 0.029411765 0.12500000 0.909090909 1.063503
## 154 2 2 0.024390244 0.11764706 0.917431193 1.059468
## 155 2 2 0.024390244 0.11764706 0.925925926 1.067963
## 156 2 2 0.024390244 0.11764706 0.925925926 1.067963
## 157 2 2 0.024390244 0.11764706 0.925925926 1.067963
## 158 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 159 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 160 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 161 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 162 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 163 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 164 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 165 2 2 0.009900990 0.03448276 1.000000000 1.044384
## 166 2 2 0.009900990 0.03448276 1.000000000 1.044384
## 167 2 2 0.009900990 0.03448276 1.000000000 1.044384
## 168 2 2 0.009900990 0.03448276 1.000000000 1.044384
## 169 2 2 0.003984064 0.02439024 1.000000000 1.028374
## 170 2 2 0.003984064 0.02439024 1.000000000 1.028374
## 171 2 2 0.003984064 0.02439024 1.000000000 1.028374
## 172 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 173 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 174 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 175 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 176 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 177 2 2 0.002849003 0.02439024 1.000000000 1.027239
## 178 2 2 0.002493766 0.01960784 1.000000000 1.022102
## 179 2 2 0.002493766 0.01960784 1.000000000 1.022102
## 180 2 2 0.002493766 0.01960784 1.000000000 1.022102
## 181 2 2 0.002217295 0.01960784 1.000000000 1.021825
## 182 0 1 0.877192982 0.12500000 0.066666667 1.068860
## 183 0 1 0.862068966 0.12500000 0.076923077 1.063992
## 184 0 1 0.862068966 0.13333333 0.076923077 1.072325
## 185 0 1 0.847457627 0.13333333 0.076923077 1.057714
## 186 0 1 0.847457627 0.14285714 0.083333333 1.073648
## 187 0 1 0.847457627 0.14285714 0.083333333 1.073648
## 188 0 1 0.847457627 0.14285714 0.083333333 1.073648
## 189 0 1 0.833333333 0.14285714 0.083333333 1.059524
## 190 0 1 0.833333333 0.15384615 0.083333333 1.070513
## 191 0 1 0.833333333 0.15384615 0.083333333 1.070513
## 192 0 1 0.819672131 0.15384615 0.083333333 1.056852
## 193 0 1 0.819672131 0.15384615 0.090909091 1.064427
## 194 0 1 0.819672131 0.15384615 0.090909091 1.064427
## 195 0 1 0.819672131 0.15384615 0.090909091 1.064427
## 196 0 1 0.819672131 0.15384615 0.083333333 1.056852
## 197 0 1 0.819672131 0.15384615 0.083333333 1.056852
## 198 0 1 0.819672131 0.15384615 0.083333333 1.056852
## 199 0 1 0.819672131 0.15384615 0.083333333 1.056852
## 200 0 1 0.833333333 0.15384615 0.076923077 1.064103
## 201 0 1 0.833333333 0.15384615 0.076923077 1.064103
## 202 0 1 0.833333333 0.15384615 0.076923077 1.064103
## 203 0 1 0.833333333 0.15384615 0.076923077 1.064103
## 204 0 1 0.833333333 0.15384615 0.076923077 1.064103
## 205 0 1 0.833333333 0.15384615 0.076923077 1.064103
## 206 1 1 0.952380952 0.07692308 0.034482759 1.063787
## 207 1 1 0.952380952 0.07692308 0.034482759 1.063787
## 208 1 1 0.943396226 0.08333333 0.038461538 1.065191
## 209 1 1 0.952380952 0.07692308 0.034482759 1.063787
## 210 1 1 0.952380952 0.08333333 0.034482759 1.070197
## 211 1 1 0.952380952 0.08333333 0.034482759 1.070197
## 212 1 1 0.952380952 0.08333333 0.034482759 1.070197
## 213 1 1 0.952380952 0.08333333 0.034482759 1.070197
## 214 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 215 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 216 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 217 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 218 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 219 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 220 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 221 1 1 0.943396226 0.09090909 0.034482759 1.068788
## 222 1 1 0.934579439 0.09090909 0.034482759 1.059971
## 223 1 1 0.934579439 0.09090909 0.034482759 1.059971
## 224 1 1 0.934579439 0.10000000 0.034482759 1.069062
## 225 1 1 0.934579439 0.10000000 0.029411765 1.063991
## 226 1 1 0.934579439 0.10000000 0.029411765 1.063991
## 227 1 1 0.952380952 0.09090909 0.029411765 1.072702
## 228 1 1 0.952380952 0.09090909 0.029411765 1.072702
## 229 1 1 0.952380952 0.09090909 0.024390244 1.067680
## 230 1 1 0.952380952 0.09090909 0.024390244 1.067680
## 231 1 1 0.952380952 0.09090909 0.024390244 1.067680
## 232 1 1 0.943396226 0.09090909 0.024390244 1.058696
## 233 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 234 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 235 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 236 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 237 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 238 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 239 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 240 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 241 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 242 1 1 0.943396226 0.10000000 0.024390244 1.067786
## 243 1 1 0.943396226 0.10526316 0.024390244 1.073050
## 244 1 1 0.943396226 0.10526316 0.024390244 1.073050
## 245 1 1 0.943396226 0.10526316 0.024390244 1.073050
## 246 1 1 0.943396226 0.10000000 0.019607843 1.063004
## 247 1 1 0.943396226 0.10526316 0.019607843 1.068267
## 248 1 1 0.943396226 0.10526316 0.019607843 1.068267
## 249 1 1 0.943396226 0.10000000 0.019607843 1.063004
## 250 1 1 0.943396226 0.10000000 0.019607843 1.063004
## 251 1 1 0.943396226 0.10000000 0.019607843 1.063004
## 252 1 1 1.000000000 0.02439024 0.003322259 1.027713
## 253 1 1 1.000000000 0.02439024 0.003322259 1.027713
## 254 1 1 1.000000000 0.02439024 0.003322259 1.027713
## 255 1 1 1.000000000 0.02439024 0.003322259 1.027713
## 256 1 1 1.000000000 0.02439024 0.003322259 1.027713
## 257 1 1 1.000000000 0.02439024 0.003322259 1.027713
## 258 1 1 1.000000000 0.02439024 0.002849003 1.027239
## 259 1 1 1.000000000 0.02439024 0.002849003 1.027239
## 260 1 1 1.000000000 0.02439024 0.002849003 1.027239
## 261 1 1 1.000000000 0.02439024 0.002493766 1.026884
## 262 1 1 1.000000000 0.01960784 0.002493766 1.022102
## 263 1 1 1.000000000 0.01960784 0.002217295 1.021825
## 264 0 2 0.322580645 0.29411765 0.434782609 1.051481
## 265 0 2 0.322580645 0.29411765 0.434782609 1.051481
## 266 0 2 0.333333333 0.29411765 0.434782609 1.062234
## 267 0 2 0.333333333 0.29411765 0.434782609 1.062234
## 268 1 2 0.333333333 0.29411765 0.421940928 1.049392
## 269 0 2 0.348432056 0.29411765 0.421940928 1.064491
## 270 0 2 0.348432056 0.30769231 0.416666667 1.072791
## 271 0 2 0.348432056 0.30769231 0.416666667 1.072791
## 272 0 2 0.348432056 0.30769231 0.400000000 1.056124
## 273 0 2 0.348432056 0.30769231 0.400000000 1.056124
## 274 0 2 0.348432056 0.30769231 0.400000000 1.056124
## 275 0 2 0.348432056 0.30769231 0.400000000 1.056124
## 276 0 2 0.348432056 0.30769231 0.400000000 1.056124
## 277 0 2 0.363636364 0.31250000 0.400000000 1.076136
## 278 0 2 0.363636364 0.31250000 0.384615385 1.060752
## 279 0 2 0.363636364 0.31250000 0.384615385 1.060752
## 280 0 2 0.363636364 0.31250000 0.384615385 1.060752
## 281 0 2 0.363636364 0.31250000 0.384615385 1.060752
## 282 0 2 0.363636364 0.32258065 0.384615385 1.070832
## 283 0 2 0.363636364 0.32258065 0.384615385 1.070832
## 284 0 2 0.363636364 0.32258065 0.381679389 1.067896
## 285 0 2 0.363636364 0.32258065 0.381679389 1.067896
## 286 0 2 0.363636364 0.32258065 0.381679389 1.067896
## 287 0 2 0.363636364 0.32258065 0.363636364 1.049853
## 288 2 2 0.363636364 0.32258065 0.363636364 1.049853
## 289 2 2 0.166666667 0.25000000 0.653594771 1.070261
## 290 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 291 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 292 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 293 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 294 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 295 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 296 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 297 2 2 0.153846154 0.25000000 0.653594771 1.057441
## 298 2 2 0.153846154 0.26666667 0.653594771 1.074108
## 299 2 2 0.153846154 0.26666667 0.653594771 1.074108
## 300 2 2 0.142857143 0.26666667 0.653594771 1.063119
## 301 2 2 0.153846154 0.26666667 0.653594771 1.074108
## 302 2 2 0.142857143 0.26666667 0.653594771 1.063119
## 303 2 2 0.142857143 0.26666667 0.666666667 1.076190
## 304 2 2 0.133333333 0.26666667 0.666666667 1.066667
## 305 2 2 0.133333333 0.26666667 0.666666667 1.066667
## 306 2 2 0.133333333 0.26666667 0.666666667 1.066667
## 307 2 2 0.133333333 0.26666667 0.666666667 1.066667
## 308 2 2 0.133333333 0.26666667 0.666666667 1.066667
## 309 2 2 0.117647059 0.25000000 0.694444444 1.062092
## 310 2 2 0.266666667 0.36363636 0.434782609 1.065086
## 311 2 2 0.100000000 0.25000000 0.714285714 1.064286
## 312 2 2 0.100000000 0.25000000 0.714285714 1.064286
## 313 2 2 0.100000000 0.25000000 0.714285714 1.064286
## 314 2 2 0.090909091 0.25000000 0.735294118 1.076203
## 315 2 2 0.090909091 0.25000000 0.735294118 1.076203
## 316 2 2 0.090909091 0.25000000 0.735294118 1.076203
## 317 2 2 0.029411765 0.08333333 0.952380952 1.065126
## 318 2 2 0.029411765 0.08333333 0.952380952 1.065126
## 319 2 2 0.029411765 0.08333333 0.952380952 1.065126
## 320 2 2 0.029411765 0.08333333 0.952380952 1.065126
## 321 2 2 0.029411765 0.08333333 0.952380952 1.065126
## 322 2 2 0.024390244 0.08333333 0.952380952 1.060105
## 323 2 2 0.024390244 0.07692308 0.961538462 1.062852
## 324 2 2 0.024390244 0.07692308 0.961538462 1.062852
## 325 2 2 0.024390244 0.07692308 0.961538462 1.062852
## 326 2 2 0.024390244 0.07692308 0.961538462 1.062852
## 327 2 2 0.012345679 0.04761905 0.990099010 1.050064
## 328 2 2 0.012345679 0.04347826 0.990099010 1.045923
## 329 2 2 0.012345679 0.04347826 0.990099010 1.045923
## 330 2 2 0.012345679 0.04347826 0.990099010 1.045923
## 331 2 2 0.012345679 0.03846154 0.990099010 1.040906
## 332 2 2 0.012345679 0.03846154 0.990099010 1.040906
## 333 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 334 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 335 2 2 0.009900990 0.03448276 1.000000000 1.044384
## 336 2 2 0.009900990 0.03448276 1.000000000 1.044384
## 337 2 2 0.003984064 0.02439024 1.000000000 1.028374
## 338 2 2 0.003984064 0.02439024 1.000000000 1.028374
## 339 2 2 0.003984064 0.02439024 1.000000000 1.028374
## 340 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 341 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 342 2 2 0.003322259 0.02439024 1.000000000 1.027713
## 343 2 2 0.002849003 0.02439024 1.000000000 1.027239
## 344 2 2 0.002849003 0.02439024 1.000000000 1.027239
## 345 2 2 0.002493766 0.01960784 1.000000000 1.022102
## 346 2 2 0.002493766 0.01960784 1.000000000 1.022102
## 347 0 1 0.714285714 0.20000000 0.133333333 1.047619
## 348 0 1 0.714285714 0.20000000 0.142857143 1.057143
## 349 0 1 0.714285714 0.20000000 0.142857143 1.057143
## 350 0 1 0.714285714 0.21052632 0.153846154 1.078658
## 351 0 1 0.714285714 0.21052632 0.153846154 1.078658
## 352 0 1 0.694444444 0.21052632 0.153846154 1.058817
## 353 0 1 0.694444444 0.21052632 0.153846154 1.058817
## 354 0 1 0.694444444 0.21052632 0.153846154 1.058817
## 355 0 1 0.694444444 0.21052632 0.153846154 1.058817
## 356 2 1 0.694444444 0.21052632 0.153846154 1.058817
## 357 0 1 0.694444444 0.22222222 0.153846154 1.070513
## 358 0 1 0.694444444 0.22222222 0.153846154 1.070513
## 359 0 1 0.694444444 0.22222222 0.153846154 1.070513
## 360 0 1 0.666666667 0.23094688 0.166666667 1.064280
## 361 0 1 0.666666667 0.23094688 0.166666667 1.064280
## 362 0 1 0.666666667 0.23094688 0.166666667 1.064280
## 363 0 1 0.666666667 0.23094688 0.166666667 1.064280
## 364 0 1 0.653594771 0.23094688 0.166666667 1.051208
## 365 0 1 0.653594771 0.23094688 0.166666667 1.051208
## 366 0 1 0.636942675 0.25000000 0.181818182 1.068761
## 367 0 1 0.636942675 0.25000000 0.181818182 1.068761
## 368 0 1 0.636942675 0.25000000 0.181818182 1.068761
## 369 0 1 0.621118012 0.25000000 0.181818182 1.052936
## 370 0 1 0.621118012 0.25000000 0.181818182 1.052936
## 371 0 1 0.621118012 0.25000000 0.181818182 1.052936
## 372 0 1 0.636942675 0.25000000 0.181818182 1.068761
## 373 0 1 0.636942675 0.26666667 0.181818182 1.085428
## 374 0 1 0.381679389 0.30769231 0.381679389 1.071051
## 375 0 1 0.400000000 0.30769231 0.348432056 1.056124
## 376 0 1 0.363636364 0.32258065 0.381679389 1.067896
## 377 0 1 0.363636364 0.32258065 0.381679389 1.067896
## 378 0 1 0.348432056 0.32258065 0.384615385 1.055628
## 379 0 1 0.348432056 0.32258065 0.400000000 1.071013
## 380 0 1 0.333333333 0.33333333 0.400000000 1.066667
## 381 0 1 0.312500000 0.33333333 0.416666667 1.062500
## 382 0 1 0.312500000 0.33333333 0.416666667 1.062500
## 383 0 1 0.322580645 0.33333333 0.416666667 1.072581
## 384 0 1 0.322580645 0.33333333 0.416666667 1.072581
## 385 0 1 0.312500000 0.33333333 0.416666667 1.062500
## 386 0 1 0.307692308 0.33333333 0.416666667 1.057692
## 387 0 1 0.307692308 0.34843206 0.416666667 1.072791
## 388 0 1 0.294117647 0.34843206 0.421940928 1.064491
## 389 0 1 0.294117647 0.34843206 0.421940928 1.064491
## 390 1 1 0.602409639 0.27777778 0.181818182 1.062006
## 391 1 1 0.602409639 0.27777778 0.181818182 1.062006
## 392 1 1 0.602409639 0.27777778 0.181818182 1.062006
## 393 1 1 0.621118012 0.27777778 0.166666667 1.065562
## 394 1 1 0.621118012 0.27777778 0.166666667 1.065562
## 395 1 1 0.581395349 0.29411765 0.200000000 1.075513
## 396 1 1 0.581395349 0.29411765 0.200000000 1.075513
## 397 1 1 0.581395349 0.29411765 0.200000000 1.075513
## 398 1 1 0.581395349 0.29411765 0.200000000 1.075513
## 399 1 1 0.581395349 0.29411765 0.200000000 1.075513
## 400 1 1 0.581395349 0.29411765 0.181818182 1.057331
## 401 1 1 0.581395349 0.29411765 0.181818182 1.057331
## 402 1 1 0.581395349 0.29411765 0.181818182 1.057331
## 403 1 1 0.581395349 0.30769231 0.181818182 1.070906
## 404 1 1 0.581395349 0.29411765 0.166666667 1.042180
## 405 1 1 0.602409639 0.29411765 0.166666667 1.063194
## 406 1 1 0.581395349 0.30769231 0.166666667 1.055754
## 407 1 1 0.602409639 0.30769231 0.166666667 1.076769
## 408 1 1 0.602409639 0.30769231 0.166666667 1.076769
## 409 1 1 0.602409639 0.30769231 0.166666667 1.076769
## 410 1 1 0.602409639 0.30769231 0.153846154 1.063948
## 411 1 1 0.602409639 0.30769231 0.153846154 1.063948
## 412 1 1 0.602409639 0.30769231 0.153846154 1.063948
## 413 1 1 0.602409639 0.30769231 0.153846154 1.063948
## 414 1 1 0.621118012 0.30769231 0.142857143 1.071667
## 415 1 1 0.621118012 0.30769231 0.133333333 1.062144
## 416 1 1 0.636942675 0.30769231 0.133333333 1.077968
## 417 1 1 0.653594771 0.29411765 0.117647059 1.065359
## 418 1 1 0.636942675 0.30769231 0.125000000 1.069635
## 419 1 1 0.636942675 0.30769231 0.117647059 1.062282
## 420 1 1 0.653594771 0.30769231 0.117647059 1.078934
## 421 1 1 0.653594771 0.29411765 0.111111111 1.058824
## 422 1 1 0.666666667 0.29411765 0.100000000 1.060784
## 423 1 1 0.694444444 0.28571429 0.090909091 1.071068
## 424 1 1 0.694444444 0.28571429 0.083333333 1.063492
## 425 1 1 0.694444444 0.28571429 0.076923077 1.057082
## 426 1 1 0.714285714 0.28571429 0.066666667 1.066667
## 427 1 1 0.694444444 0.29411765 0.066666667 1.055229
## 428 1 1 0.735294118 0.28571429 0.052631579 1.073640
## 429 1 1 0.714285714 0.29411765 0.052631579 1.061035
## 430 1 1 0.751879699 0.27777778 0.043478261 1.073136
## 431 1 1 0.751879699 0.26666667 0.038461538 1.057008
## 432 1 1 0.769230769 0.26666667 0.034482759 1.070380
## 433 1 1 0.781250000 0.26666667 0.029411765 1.077328
## 434 1 1 0.781250000 0.25000000 0.029411765 1.060662
## 435 1 1 0.800000000 0.25000000 0.024390244 1.074390
## 436 1 1 0.819672131 0.23094688 0.024390244 1.075009
## 437 1 1 0.833333333 0.21052632 0.019607843 1.063467
## 438 1 1 0.833333333 0.21052632 0.019607843 1.063467
## 439 1 1 0.847457627 0.21052632 0.019607843 1.077592
## 440 1 1 0.900900901 0.15384615 0.009900990 1.064648
## 441 1 1 0.892857143 0.16666667 0.014925373 1.074449
## 442 1 1 0.900900901 0.15384615 0.014925373 1.069672
## 443 1 1 0.961538462 0.07692308 0.002849003 1.041311
## 444 0 0 0.454545455 0.29411765 0.307692308 1.056355
## 445 0 0 0.454545455 0.29411765 0.307692308 1.056355
## 446 0 0 0.454545455 0.29411765 0.307692308 1.056355
## 447 0 0 0.454545455 0.29411765 0.312500000 1.061163
## 448 0 0 0.454545455 0.29411765 0.312500000 1.061163
## 449 0 0 0.454545455 0.29411765 0.312500000 1.061163
## 450 0 0 0.454545455 0.29411765 0.312500000 1.061163
## 451 0 0 0.444444444 0.29411765 0.312500000 1.051062
## 452 0 0 0.444444444 0.30769231 0.322580645 1.074717
## 453 0 0 0.444444444 0.30769231 0.322580645 1.074717
## 454 0 0 0.434782609 0.30769231 0.322580645 1.065056
## 455 0 0 0.434782609 0.30769231 0.322580645 1.065056
## 456 0 0 0.434782609 0.30769231 0.322580645 1.065056
## 457 0 0 0.421940928 0.30769231 0.322580645 1.052214
## 458 0 0 0.434782609 0.30769231 0.322580645 1.065056
## 459 0 0 0.434782609 0.30769231 0.322580645 1.065056
## 460 0 0 0.434782609 0.30769231 0.322580645 1.065056
## 461 0 0 0.434782609 0.30769231 0.322580645 1.065056
## 462 0 0 0.421940928 0.31250000 0.322580645 1.057022
## 463 0 0 0.421940928 0.31250000 0.322580645 1.057022
## 464 0 0 0.421940928 0.31250000 0.322580645 1.057022
## 465 0 0 0.421940928 0.32258065 0.322580645 1.067102
## 466 1 0 0.694444444 0.25000000 0.142857143 1.087302
## 467 1 0 0.666666667 0.25000000 0.142857143 1.059524
## 468 1 0 0.694444444 0.25000000 0.133333333 1.077778
## 469 1 0 0.694444444 0.25000000 0.133333333 1.077778
## 470 1 0 0.694444444 0.23094688 0.125000000 1.050391
## 471 1 0 0.714285714 0.23094688 0.125000000 1.070233
## 472 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 473 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 474 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 475 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 476 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 477 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 478 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 479 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 480 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 481 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 482 1 0 0.714285714 0.23094688 0.111111111 1.056344
## 483 1 0 0.714285714 0.23094688 0.111111111 1.056344
## 484 1 0 0.714285714 0.23094688 0.111111111 1.056344
## 485 1 0 0.714285714 0.23094688 0.111111111 1.056344
## 486 1 0 0.714285714 0.23094688 0.111111111 1.056344
## 487 1 0 0.714285714 0.23094688 0.111111111 1.056344
## 488 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 489 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 490 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 491 1 0 0.714285714 0.23094688 0.117647059 1.062880
## 492 1 0 0.714285714 0.25000000 0.117647059 1.081933
## 493 1 0 0.666666667 0.25000000 0.133333333 1.050000
## 494 1 0 0.694444444 0.25000000 0.117647059 1.062092
## 495 1 0 0.714285714 0.25000000 0.111111111 1.075397
## 496 1 0 0.714285714 0.25000000 0.111111111 1.075397
## 497 1 0 0.714285714 0.25000000 0.111111111 1.075397
## 498 1 0 0.714285714 0.25000000 0.105263158 1.069549
## 499 1 0 0.714285714 0.25000000 0.105263158 1.069549
## 500 1 0 0.714285714 0.25000000 0.105263158 1.069549
## 501 1 0 0.714285714 0.25000000 0.105263158 1.069549
## 502 1 0 0.714285714 0.25000000 0.105263158 1.069549
## 503 1 0 0.714285714 0.25000000 0.105263158 1.069549
## 504 1 0 0.714285714 0.25000000 0.105263158 1.069549
## 505 1 0 0.714285714 0.25000000 0.100000000 1.064286
## 506 1 0 0.714285714 0.25000000 0.100000000 1.064286
## 507 1 0 0.735294118 0.25000000 0.090909091 1.076203
## 508 1 0 0.735294118 0.25000000 0.090909091 1.076203
## 509 1 0 0.735294118 0.25000000 0.090909091 1.076203
## 510 1 0 0.735294118 0.25000000 0.083333333 1.068627
## 511 1 0 0.751879699 0.23094688 0.076923077 1.059750
## 512 1 0 0.751879699 0.23094688 0.066666667 1.049493
## 513 1 0 0.751879699 0.23094688 0.066666667 1.049493
## 514 1 0 0.751879699 0.23094688 0.066666667 1.049493
## 515 1 0 0.769230769 0.23094688 0.066666667 1.066844
## 516 1 0 0.781250000 0.23094688 0.058823529 1.071020
## 517 1 0 0.781250000 0.23094688 0.052631579 1.064828
## 518 1 0 0.781250000 0.23094688 0.047619048 1.059816
## 519 1 0 0.781250000 0.23094688 0.047619048 1.059816
## 520 1 0 0.800000000 0.23094688 0.043478261 1.074425
## 521 1 0 0.800000000 0.22222222 0.038461538 1.060684
## 522 1 0 0.800000000 0.22222222 0.038461538 1.060684
## 523 1 0 0.800000000 0.22222222 0.034482759 1.056705
## 524 1 0 0.800000000 0.22222222 0.034482759 1.056705
## 525 1 0 0.819672131 0.22222222 0.029411765 1.071306
## 526 1 0 0.819672131 0.22222222 0.029411765 1.071306
## 527 1 0 0.819672131 0.21052632 0.024390244 1.054589
## 528 1 0 0.847457627 0.20000000 0.024390244 1.071848
## 529 1 0 0.862068966 0.18181818 0.019607843 1.063495
## 530 1 0 0.862068966 0.18181818 0.019607843 1.063495
## 531 1 0 0.877192982 0.18181818 0.019607843 1.078619
## 532 1 0 0.892857143 0.16666667 0.014925373 1.074449
## 533 1 0 0.892857143 0.16666667 0.014925373 1.074449
## 534 0 0 0.153846154 0.78125000 0.133333333 1.068429
## 535 0 0 0.133333333 0.81967213 0.117647059 1.070653
## 536 0 0 0.125000000 0.81967213 0.117647059 1.062319
## 537 0 0 0.117647059 0.83333333 0.111111111 1.062092
## 538 0 0 0.100000000 0.86206897 0.105263158 1.067332
## 539 0 0 0.083333333 0.90909091 0.076923077 1.069347
## 540 0 0 0.066666667 0.93457944 0.066666667 1.067913
## 541 0 0 0.052631579 0.96153846 0.047619048 1.061789
## 542 0 2 0.416666667 0.28571429 0.363636364 1.066017
## 543 0 2 0.416666667 0.28571429 0.363636364 1.066017
## 544 0 2 0.416666667 0.28571429 0.363636364 1.066017
## 545 0 2 0.210526316 0.25000000 0.621118012 1.081644
## 546 2 2 0.222222222 0.25000000 0.602409639 1.074632
## 547 2 2 0.222222222 0.25000000 0.602409639 1.074632
## 548 2 2 0.222222222 0.25000000 0.602409639 1.074632
## 549 2 2 0.210526316 0.25000000 0.602409639 1.062936
## 550 2 2 0.210526316 0.25000000 0.602409639 1.062936
## 551 2 2 0.210526316 0.25000000 0.602409639 1.062936
## 552 2 2 0.210526316 0.25000000 0.602409639 1.062936
## 553 2 2 0.210526316 0.25000000 0.602409639 1.062936
## 554 2 2 0.210526316 0.25000000 0.602409639 1.062936
## 555 2 2 0.200000000 0.25000000 0.602409639 1.052410
## 556 2 2 0.200000000 0.25000000 0.621118012 1.071118
## 557 2 2 0.200000000 0.25000000 0.621118012 1.071118
## 558 2 2 0.200000000 0.25000000 0.621118012 1.071118
## 559 2 2 0.181818182 0.25000000 0.621118012 1.052936
## 560 2 2 0.181818182 0.25000000 0.621118012 1.052936
## 561 2 2 0.181818182 0.25000000 0.621118012 1.052936
## 562 2 2 0.181818182 0.25000000 0.621118012 1.052936
## 563 2 2 0.181818182 0.25000000 0.621118012 1.052936
## 564 2 2 0.181818182 0.25000000 0.636942675 1.068761
## 565 2 2 0.181818182 0.25000000 0.636942675 1.068761
## 566 2 2 0.181818182 0.25000000 0.636942675 1.068761
## 567 2 2 0.181818182 0.25000000 0.636942675 1.068761
## 568 2 2 0.166666667 0.25000000 0.653594771 1.070261
## 569 2 2 0.166666667 0.25000000 0.653594771 1.070261
## 570 2 2 0.166666667 0.25000000 0.653594771 1.070261
## 571 2 2 0.166666667 0.25000000 0.636942675 1.053609
## 572 2 2 0.166666667 0.25000000 0.653594771 1.070261
## 573 2 2 0.153846154 0.25000000 0.666666667 1.070513
## 574 2 2 0.153846154 0.25000000 0.666666667 1.070513
## 575 2 2 0.153846154 0.25000000 0.666666667 1.070513
## 576 2 2 0.153846154 0.25000000 0.666666667 1.070513
## 577 2 2 0.307692308 0.32258065 0.434782609 1.065056
## 578 0 2 0.363636364 0.34843206 0.348432056 1.060500
## 579 0 2 0.363636364 0.34843206 0.348432056 1.060500
## 580 0 2 0.363636364 0.34843206 0.363636364 1.075705
## 581 0 2 0.363636364 0.34843206 0.348432056 1.060500
## 582 0 2 0.363636364 0.34843206 0.348432056 1.060500
## 583 0 2 0.363636364 0.36363636 0.348432056 1.075705
## 584 0 2 0.348432056 0.36363636 0.348432056 1.060500
## 585 0 2 0.348432056 0.36363636 0.348432056 1.060500
## 586 0 2 0.348432056 0.36363636 0.348432056 1.060500
## 587 0 2 0.348432056 0.36363636 0.348432056 1.060500
## 588 0 2 0.348432056 0.36363636 0.348432056 1.060500
## 589 0 2 0.333333333 0.38461538 0.333333333 1.051282
## 590 0 2 0.333333333 0.38461538 0.333333333 1.051282
## 591 0 2 0.333333333 0.40000000 0.333333333 1.066667
## 592 0 2 0.333333333 0.40000000 0.333333333 1.066667
## 593 0 2 0.322580645 0.40000000 0.333333333 1.055914
## 594 0 2 0.322580645 0.40000000 0.333333333 1.055914
## 595 0 2 0.322580645 0.41666667 0.322580645 1.061828
## 596 0 2 0.322580645 0.41666667 0.322580645 1.061828
## 597 0 2 0.322580645 0.41666667 0.322580645 1.061828
## 598 0 2 0.322580645 0.43478261 0.307692308 1.065056
## 599 0 2 0.322580645 0.43478261 0.312500000 1.069863
## 600 0 2 0.312500000 0.43478261 0.312500000 1.059783
## 601 0 2 0.312500000 0.44444444 0.307692308 1.064637
## 602 0 2 0.307692308 0.45454545 0.307692308 1.069930
## 603 0 2 0.307692308 0.45454545 0.294117647 1.056355
## 604 0 2 0.294117647 0.47619048 0.294117647 1.064426
## 605 0 2 0.294117647 0.47619048 0.285714286 1.056022
## 606 0 2 0.294117647 0.47619048 0.294117647 1.064426
## 607 0 2 0.294117647 0.48780488 0.277777778 1.059700
## 608 0 2 0.294117647 0.48780488 0.277777778 1.059700
## 609 0 2 0.285714286 0.51282051 0.266666667 1.065201
## 610 0 2 0.285714286 0.51282051 0.266666667 1.065201
## 611 0 2 0.277777778 0.52631579 0.266666667 1.070760
## 612 0 2 0.266666667 0.52631579 0.266666667 1.059649
## 613 0 2 0.266666667 0.54644809 0.250000000 1.063115
## 614 0 2 0.250000000 0.54644809 0.266666667 1.063115
## 615 0 2 0.250000000 0.54644809 0.266666667 1.063115
## 616 0 2 0.250000000 0.58139535 0.250000000 1.081395
## 617 0 2 0.230946882 0.60240964 0.230946882 1.064303
## 618 0 2 0.230946882 0.60240964 0.230946882 1.064303
## 619 0 2 0.230946882 0.62111801 0.222222222 1.074287
## 620 0 2 0.230946882 0.62111801 0.210526316 1.062591
## 621 0 2 0.034482759 0.23094688 0.800000000 1.065430
## 622 2 2 0.029411765 0.22222222 0.819672131 1.071306
## 623 2 2 0.029411765 0.22222222 0.819672131 1.071306
## 624 2 2 0.029411765 0.22222222 0.819672131 1.071306
## 625 2 2 0.024390244 0.21052632 0.833333333 1.068250
## 626 2 2 0.024390244 0.21052632 0.833333333 1.068250
## 627 2 2 0.024390244 0.20000000 0.847457627 1.071848
## 628 2 2 0.019607843 0.18181818 0.862068966 1.063495
## 629 2 2 0.019607843 0.18181818 0.877192982 1.078619
## 630 2 2 0.014925373 0.16666667 0.892857143 1.074449
## 631 2 2 0.012345679 0.15384615 0.900900901 1.067093
## 632 2 2 0.012345679 0.15384615 0.900900901 1.067093
## 633 2 2 0.019607843 0.18181818 0.877192982 1.078619
## 634 2 2 0.012345679 0.14285714 0.909090909 1.064294
## 635 2 2 0.007936508 0.11111111 0.934579439 1.053627
## 636 2 2 0.006622517 0.10000000 0.943396226 1.050019
## 637 2 2 0.004975124 0.10000000 0.943396226 1.048371
## 638 2 2 0.003322259 0.07692308 0.961538462 1.041784
## 639 2 2 0.001996008 0.05882353 0.980392157 1.041212
## 640 0 1 0.363636364 0.30769231 0.381679389 1.053008
## 641 0 1 0.363636364 0.30769231 0.381679389 1.053008
## 642 0 1 0.363636364 0.30769231 0.384615385 1.055944
## 643 0 1 0.363636364 0.31250000 0.400000000 1.076136
## 644 0 1 0.363636364 0.31250000 0.400000000 1.076136
## 645 0 1 0.363636364 0.31250000 0.384615385 1.060752
## 646 0 1 0.363636364 0.31250000 0.384615385 1.060752
## 647 0 1 0.348432056 0.31250000 0.400000000 1.060932
## 648 0 1 0.348432056 0.32258065 0.400000000 1.071013
## 649 0 1 0.348432056 0.32258065 0.400000000 1.071013
## 650 0 1 0.348432056 0.32258065 0.400000000 1.071013
## 651 0 1 0.333333333 0.32258065 0.400000000 1.055914
## 652 0 1 0.322580645 0.32258065 0.416666667 1.061828
## 653 0 1 0.322580645 0.32258065 0.416666667 1.061828
## 654 0 1 0.322580645 0.32258065 0.416666667 1.061828
## 655 0 1 0.312500000 0.33333333 0.416666667 1.062500
## 656 0 1 0.312500000 0.33333333 0.416666667 1.062500
## 657 0 1 0.307692308 0.33333333 0.421940928 1.062967
## 658 0 1 0.307692308 0.33333333 0.421940928 1.062967
## 659 0 1 0.307692308 0.33333333 0.416666667 1.057692
## 660 0 1 0.294117647 0.33333333 0.444444444 1.071895
## 661 0 1 0.294117647 0.34843206 0.421940928 1.064491
## 662 0 1 0.307692308 0.34843206 0.416666667 1.072791
## 663 0 1 0.307692308 0.34843206 0.400000000 1.056124
## 664 0 1 0.307692308 0.34843206 0.400000000 1.056124
## 665 0 1 0.307692308 0.34843206 0.400000000 1.056124
## 666 1 1 0.307692308 0.34843206 0.400000000 1.056124
## 667 1 1 0.581395349 0.28571429 0.200000000 1.067110
## 668 1 1 0.581395349 0.28571429 0.200000000 1.067110
## 669 1 1 0.581395349 0.28571429 0.200000000 1.067110
## 670 1 1 0.581395349 0.28571429 0.181818182 1.048928
## 671 1 1 0.581395349 0.28571429 0.181818182 1.048928
## 672 1 1 0.602409639 0.28571429 0.181818182 1.069942
## 673 1 1 0.602409639 0.28571429 0.181818182 1.069942
## 674 1 1 0.602409639 0.28571429 0.181818182 1.069942
## 675 1 1 0.602409639 0.28571429 0.166666667 1.054791
## 676 1 1 0.602409639 0.28571429 0.166666667 1.054791
## 677 1 1 0.621118012 0.28571429 0.166666667 1.073499
## 678 1 1 0.621118012 0.28571429 0.166666667 1.073499
## 679 1 1 0.621118012 0.27777778 0.153846154 1.052742
## 680 1 1 0.636942675 0.27777778 0.153846154 1.068567
## 681 1 1 0.653594771 0.27777778 0.142857143 1.074230
## 682 1 1 0.653594771 0.27777778 0.142857143 1.074230
## 683 1 1 0.636942675 0.27777778 0.142857143 1.057578
## 684 1 1 0.653594771 0.27777778 0.142857143 1.074230
## 685 1 1 0.653594771 0.27777778 0.133333333 1.064706
## 686 1 1 0.653594771 0.27777778 0.133333333 1.064706
## 687 1 1 0.653594771 0.27777778 0.133333333 1.064706
## 688 1 1 0.653594771 0.27777778 0.133333333 1.064706
## 689 1 1 0.653594771 0.27777778 0.133333333 1.064706
## 690 1 1 0.666666667 0.27777778 0.125000000 1.069444
## 691 1 1 0.666666667 0.27777778 0.125000000 1.069444
## 692 1 1 0.666666667 0.27777778 0.125000000 1.069444
## 693 1 1 0.666666667 0.27777778 0.117647059 1.062092
## 694 1 1 0.666666667 0.27777778 0.117647059 1.062092
## 695 0 1 0.266666667 0.45454545 0.333333333 1.054545
## 696 0 1 0.266666667 0.48780488 0.322580645 1.077052
## 697 0 1 0.250000000 0.50000000 0.312500000 1.062500
## 698 0 1 0.250000000 0.50000000 0.307692308 1.057692
## 699 0 1 0.250000000 0.51282051 0.307692308 1.070513
## 700 0 1 0.250000000 0.51282051 0.307692308 1.070513
## 701 0 1 0.230946882 0.51282051 0.312500000 1.056267
## 702 0 1 0.230946882 0.52631579 0.307692308 1.064955
## 703 0 1 0.230946882 0.52631579 0.307692308 1.064955
## 704 0 1 0.230946882 0.52631579 0.307692308 1.064955
## 705 0 1 0.222222222 0.54644809 0.294117647 1.062788
## 706 0 1 0.222222222 0.55555556 0.285714286 1.063492
## 707 0 1 0.210526316 0.55555556 0.294117647 1.060200
## 708 0 1 0.210526316 0.58139535 0.277777778 1.069699
## 709 0 1 0.200000000 0.58139535 0.277777778 1.059173
## 710 0 1 0.200000000 0.60240964 0.266666667 1.069076
## 711 0 1 0.210526316 0.60240964 0.250000000 1.062936
## 712 1 1 0.800000000 0.23094688 0.034482759 1.065430
## 713 1 1 0.800000000 0.22222222 0.029411765 1.051634
## 714 1 1 0.800000000 0.23094688 0.034482759 1.065430
## 715 1 1 0.819672131 0.22222222 0.024390244 1.066285
## 716 1 1 0.833333333 0.21052632 0.024390244 1.068250
## 717 1 1 0.819672131 0.21052632 0.024390244 1.054589
## 718 1 1 0.847457627 0.20000000 0.019607843 1.067065
## 719 1 1 0.862068966 0.20000000 0.019607843 1.081677
## 720 1 1 0.877192982 0.18181818 0.019607843 1.078619
## 721 1 1 0.877192982 0.18181818 0.014925373 1.073937
## 722 1 1 0.892857143 0.16666667 0.014925373 1.074449
## 723 1 1 0.900900901 0.15384615 0.009900990 1.064648
## 724 1 1 0.925925926 0.13333333 0.009900990 1.069160
## 725 1 1 0.925925926 0.12500000 0.007936508 1.058862
## 726 1 1 0.952380952 0.09090909 0.003984064 1.047274
## 727 1 1 0.961538462 0.07692308 0.002849003 1.041311
## 728 1 1 0.980392157 0.05882353 0.001996008 1.041212
## 729 1 1 0.990099010 0.04347826 0.001996008 1.035573
## 730 0 2 0.277777778 0.25000000 0.512820513 1.040598
## 731 0 2 0.277777778 0.25000000 0.512820513 1.040598
## 732 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 733 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 734 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 735 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 736 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 737 0 2 0.285714286 0.25000000 0.526315789 1.062030
## 738 0 2 0.277777778 0.26666667 0.526315789 1.070760
## 739 0 2 0.277777778 0.26666667 0.526315789 1.070760
## 740 0 2 0.277777778 0.26666667 0.526315789 1.070760
## 741 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 742 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 743 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 744 0 2 0.277777778 0.25000000 0.526315789 1.054094
## 745 0 2 0.266666667 0.25000000 0.546448087 1.063115
## 746 0 2 0.266666667 0.25000000 0.546448087 1.063115
## 747 2 2 0.142857143 0.21052632 0.714285714 1.067669
## 748 2 2 0.125000000 0.20000000 0.735294118 1.060294
## 749 2 2 0.125000000 0.20000000 0.735294118 1.060294
## 750 2 2 0.117647059 0.20000000 0.751879699 1.069527
## 751 2 2 0.111111111 0.20000000 0.751879699 1.062991
## 752 2 2 0.111111111 0.20000000 0.751879699 1.062991
## 753 2 2 0.111111111 0.20000000 0.751879699 1.062991
## 754 2 2 0.111111111 0.20000000 0.751879699 1.062991
## 755 2 2 0.111111111 0.20000000 0.751879699 1.062991
## 756 2 2 0.105263158 0.20000000 0.769230769 1.074494
## 757 2 2 0.105263158 0.20000000 0.769230769 1.074494
## 758 2 2 0.105263158 0.20000000 0.769230769 1.074494
## 759 2 2 0.105263158 0.20000000 0.769230769 1.074494
## 760 2 2 0.105263158 0.20000000 0.769230769 1.074494
## 761 2 2 0.105263158 0.20000000 0.769230769 1.074494
## 762 2 2 0.105263158 0.20000000 0.769230769 1.074494
## 763 2 2 0.105263158 0.20000000 0.751879699 1.057143
## 764 2 2 0.100000000 0.20000000 0.769230769 1.069231
## 765 2 2 0.100000000 0.20000000 0.769230769 1.069231
## 766 2 2 0.100000000 0.20000000 0.769230769 1.069231
## 767 2 2 0.100000000 0.20000000 0.769230769 1.069231
## 768 2 2 0.090909091 0.20000000 0.769230769 1.060140
## 769 2 2 0.090909091 0.20000000 0.781250000 1.072159
## 770 2 2 0.090909091 0.20000000 0.781250000 1.072159
## 771 2 2 0.090909091 0.20000000 0.781250000 1.072159
## 772 2 2 0.090909091 0.20000000 0.769230769 1.060140
## 773 2 2 0.090909091 0.20000000 0.769230769 1.060140
## 774 2 2 0.090909091 0.20000000 0.769230769 1.060140
## 775 2 2 0.090909091 0.21052632 0.769230769 1.070666
## 776 2 2 0.090909091 0.21052632 0.769230769 1.070666
## 777 2 2 0.105263158 0.21052632 0.751879699 1.067669
## 778 2 2 0.100000000 0.21052632 0.751879699 1.062406
## 779 2 2 0.100000000 0.21052632 0.751879699 1.062406
## 780 2 2 0.100000000 0.21052632 0.751879699 1.062406
## 781 2 2 0.100000000 0.21052632 0.751879699 1.062406
## 782 2 2 0.090909091 0.21052632 0.751879699 1.053315
## 783 2 2 0.090909091 0.21052632 0.769230769 1.070666
## 784 2 2 0.090909091 0.21052632 0.769230769 1.070666
## 785 2 2 0.090909091 0.21052632 0.769230769 1.070666
## 786 2 2 0.083333333 0.21052632 0.769230769 1.063090
## 787 2 2 0.083333333 0.21052632 0.769230769 1.063090
## 788 2 2 0.076923077 0.21052632 0.781250000 1.068699
## 789 2 2 0.076923077 0.21052632 0.781250000 1.068699
## 790 2 2 0.076923077 0.21052632 0.781250000 1.068699
## 791 2 2 0.076923077 0.21052632 0.781250000 1.068699
## 792 2 2 0.076923077 0.21052632 0.781250000 1.068699
## 793 2 2 0.076923077 0.22222222 0.769230769 1.068376
## 794 2 2 0.076923077 0.22222222 0.769230769 1.068376
## 795 2 2 0.076923077 0.22222222 0.769230769 1.068376
## 796 2 2 0.076923077 0.22222222 0.769230769 1.068376
## 797 2 2 0.066666667 0.22222222 0.781250000 1.070139
## 798 2 2 0.066666667 0.22222222 0.781250000 1.070139
## 799 2 2 0.066666667 0.22222222 0.781250000 1.070139
## 800 2 2 0.066666667 0.22222222 0.781250000 1.070139
## 801 2 2 0.058823529 0.22222222 0.781250000 1.062296
## 802 2 2 0.058823529 0.22222222 0.781250000 1.062296
## 803 2 2 0.058823529 0.21052632 0.800000000 1.069350
## 804 2 2 0.058823529 0.21052632 0.800000000 1.069350
## 805 2 2 0.052631579 0.21052632 0.800000000 1.063158
## 806 2 2 0.052631579 0.21052632 0.800000000 1.063158
## 807 2 2 0.043478261 0.20000000 0.819672131 1.063150
## 808 2 2 0.038461538 0.20000000 0.833333333 1.071795
## 809 2 2 0.038461538 0.20000000 0.833333333 1.071795
## 810 2 2 0.029411765 0.20000000 0.847457627 1.076869
## 811 2 2 0.029411765 0.20000000 0.847457627 1.076869
## 812 2 2 0.024390244 0.18181818 0.862068966 1.068277
## 813 2 2 0.024390244 0.18181818 0.877192982 1.083401
## 814 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 815 2 2 0.009900990 0.03846154 1.000000000 1.048363
## 816 2 2 0.002849003 0.02439024 1.000000000 1.027239
## 817 2 2 0.002849003 0.02439024 1.000000000 1.027239
## 818 2 2 0.002493766 0.01960784 1.000000000 1.022102
## 819 2 2 0.002217295 0.01960784 1.000000000 1.021825
## 820 0 0 0.222222222 0.23094688 0.602409639 1.055579
## 821 0 0 0.222222222 0.23094688 0.602409639 1.055579
## 822 0 0 0.230946882 0.23094688 0.602409639 1.064303
## 823 0 0 0.230946882 0.25000000 0.602409639 1.083357
## 824 0 0 0.230946882 0.25000000 0.602409639 1.083357
## 825 0 0 0.222222222 0.23094688 0.602409639 1.055579
## 826 0 0 0.210526316 0.23094688 0.621118012 1.062591
## 827 0 0 0.200000000 0.23094688 0.621118012 1.052065
## 828 0 0 0.200000000 0.23094688 0.621118012 1.052065
## 829 0 0 0.200000000 0.23094688 0.621118012 1.052065
## 830 0 0 0.200000000 0.23094688 0.621118012 1.052065
## 831 0 0 0.200000000 0.23094688 0.636942675 1.067890
## 832 0 0 0.181818182 0.23094688 0.636942675 1.049708
## 833 0 0 0.200000000 0.23094688 0.636942675 1.067890
## 834 0 0 0.200000000 0.23094688 0.636942675 1.067890
## 835 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 836 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 837 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 838 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 839 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 840 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 841 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 842 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 843 0 0 0.200000000 0.25000000 0.621118012 1.071118
## 844 0 0 0.181818182 0.25000000 0.621118012 1.052936
## 845 0 0 0.181818182 0.25000000 0.621118012 1.052936
## 846 0 0 0.181818182 0.26666667 0.621118012 1.069603
## 847 0 0 0.181818182 0.26666667 0.621118012 1.069603
## 848 2 0 0.090909091 0.18181818 0.800000000 1.072727
## 849 2 0 0.083333333 0.16666667 0.800000000 1.050000
## 850 2 0 0.083333333 0.16666667 0.819672131 1.069672
## 851 2 0 0.076923077 0.16666667 0.819672131 1.063262
## 852 2 0 0.076923077 0.16666667 0.819672131 1.063262
## 853 2 0 0.076923077 0.16666667 0.819672131 1.063262
## 854 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 855 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 856 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 857 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 858 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 859 2 0 0.076923077 0.16666667 0.819672131 1.063262
## 860 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 861 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 862 2 0 0.066666667 0.16666667 0.833333333 1.066667
## 863 2 0 0.058823529 0.15384615 0.847457627 1.060127
## 864 2 0 0.052631579 0.15384615 0.847457627 1.053935
## 865 2 0 0.052631579 0.15384615 0.862068966 1.068547
## 866 2 0 0.052631579 0.15384615 0.862068966 1.068547
## 867 2 0 0.047619048 0.15384615 0.862068966 1.063534
## 868 2 0 0.047619048 0.15384615 0.862068966 1.063534
## 869 2 0 0.047619048 0.15384615 0.862068966 1.063534
## 870 2 0 0.047619048 0.15384615 0.877192982 1.078658
## 871 2 0 0.047619048 0.15384615 0.877192982 1.078658
## 872 2 0 0.047619048 0.15384615 0.877192982 1.078658
## 873 2 0 0.043478261 0.15384615 0.877192982 1.074517
## 874 2 0 0.043478261 0.14285714 0.877192982 1.063528
## 875 2 0 0.043478261 0.14285714 0.877192982 1.063528
## 876 0 0 0.133333333 0.38167939 0.546448087 1.061461
## 877 0 0 0.125000000 0.38461538 0.546448087 1.056063
## 878 0 0 0.133333333 0.40000000 0.526315789 1.059649
## 879 0 0 0.142857143 0.40000000 0.526315789 1.069173
## 880 0 0 0.142857143 0.40000000 0.512820513 1.055678
## 881 0 0 0.142857143 0.42194093 0.487804878 1.052603
## 882 0 0 0.142857143 0.43478261 0.476190476 1.053830
## 883 0 0 0.153846154 0.44444444 0.454545455 1.052836
## 884 0 0 0.153846154 0.45454545 0.454545455 1.062937
## 885 0 0 0.153846154 0.45454545 0.454545455 1.062937
## 886 0 0 0.166666667 0.47619048 0.434782609 1.077640
## 887 0 0 0.166666667 0.48780488 0.421940928 1.076412
## 888 0 0 0.153846154 0.50000000 0.416666667 1.070513
## 889 0 0 0.142857143 0.52631579 0.400000000 1.069173
## 890 0 0 0.142857143 0.54644809 0.381679389 1.070985
## 891 0 0 0.153846154 0.54644809 0.363636364 1.063931
## 892 0 0 0.142857143 0.55555556 0.363636364 1.062049
## P_home_norm P_draw_norm P_away_norm total_minute goal_difference
## 1 0.572409845 0.23755009 0.190040069 0 0
## 2 0.572409845 0.23755009 0.190040069 1 0
## 3 0.589891406 0.23743129 0.172677303 2 0
## 4 0.579878226 0.23340099 0.186720789 3 0
## 5 0.579878226 0.23340099 0.186720789 4 0
## 6 0.579878226 0.23340099 0.186720789 5 0
## 7 0.589891406 0.23743129 0.172677303 6 0
## 8 0.579878226 0.23340099 0.186720789 7 0
## 9 0.570993529 0.24514656 0.183859916 8 0
## 10 0.557992012 0.24700446 0.195003524 9 0
## 11 0.563486101 0.24943651 0.187077385 10 0
## 12 0.580699655 0.24931372 0.169986626 11 0
## 13 0.580699655 0.24931372 0.169986626 12 0
## 14 0.580699655 0.24931372 0.169986626 13 0
## 15 0.595963700 0.23391575 0.170120547 14 0
## 16 0.580699655 0.24931372 0.169986626 15 0
## 17 0.580699655 0.24931372 0.169986626 16 0
## 18 0.580699655 0.24931372 0.169986626 17 0
## 19 0.573235131 0.25375208 0.173012785 18 0
## 20 0.573235131 0.25375208 0.173012785 19 0
## 21 0.573235131 0.25375208 0.173012785 20 0
## 22 0.567237724 0.26155962 0.171202659 21 0
## 23 0.567237724 0.26155962 0.171202659 22 0
## 24 0.567237724 0.26155962 0.171202659 23 0
## 25 0.567237724 0.26155962 0.171202659 24 0
## 26 0.567237724 0.26155962 0.171202659 25 0
## 27 0.563030126 0.26703715 0.169932729 26 0
## 28 0.571117759 0.27087299 0.158009247 27 0
## 29 0.571117759 0.27087299 0.158009247 28 0
## 30 0.585585586 0.26936937 0.145045045 29 0
## 31 0.585585586 0.26936937 0.145045045 30 0
## 32 0.585585586 0.26936937 0.145045045 31 0
## 33 0.585585586 0.26936937 0.145045045 32 0
## 34 0.580982676 0.27511238 0.143904940 33 0
## 35 0.580982676 0.27511238 0.143904940 34 0
## 36 0.580982676 0.27511238 0.143904940 35 0
## 37 0.580982676 0.27511238 0.143904940 36 0
## 38 0.580982676 0.27511238 0.143904940 37 0
## 39 0.587016575 0.27796961 0.135013812 38 0
## 40 0.587016575 0.27796961 0.135013812 39 0
## 41 0.566202091 0.28919861 0.144599303 40 0
## 42 0.563655086 0.29239608 0.143948837 41 0
## 43 0.563655086 0.29239608 0.143948837 42 0
## 44 0.558388295 0.29900793 0.142603780 43 0
## 45 0.564134560 0.30208496 0.133780481 44 0
## 46 0.564134560 0.30208496 0.133780481 45 0
## 47 0.544084821 0.31194196 0.143973214 46 0
## 48 0.518893509 0.32543844 0.155668053 47 0
## 49 0.518893509 0.32543844 0.155668053 48 0
## 50 0.507497116 0.33771626 0.154786621 49 0
## 51 0.498113208 0.34415094 0.157735849 50 0
## 52 0.484581498 0.34361233 0.171806167 51 0
## 53 0.470146819 0.35889070 0.170962480 52 0
## 54 0.476458140 0.35461579 0.168926068 53 0
## 55 0.468852459 0.36065574 0.170491803 54 0
## 56 0.481927711 0.36144578 0.156626506 55 0
## 57 0.475059382 0.37054632 0.154394299 56 0
## 58 0.480769231 0.37500000 0.144230769 57 0
## 59 0.480769231 0.37500000 0.144230769 58 0
## 60 0.467065868 0.38922156 0.143712575 59 0
## 61 0.471910112 0.39325843 0.134831461 60 0
## 62 0.471910112 0.39325843 0.134831461 61 0
## 63 0.463427239 0.40085478 0.135717977 62 0
## 64 0.451807229 0.42168675 0.126506024 63 0
## 65 0.447203111 0.40831588 0.144481005 64 0
## 66 0.432098765 0.43209877 0.135802469 65 0
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## [ reached 'max' / getOption("max.print") -- omitted 55235 rows ]match_data$match_start_datetime <- as.Date(match_data$match_start_datetime, format = "%d.%m.%Y")
training_list <- match_data$fixture_id[match_data$match_start_datetime < as.Date("2024-11-01")]
test_list <- match_data$fixture_id[match_data$match_start_datetime >= as.Date("2024-11-01")]
last_training_data <- cleaned_data[cleaned_data$fixture_id %in% training_list, ]
last_test_data <- cleaned_data[cleaned_data$fixture_id %in% test_list, ]ggplot(last_training_data, aes(x = total_minute, y = home_away_diff, color = category, group = fixture_id)) +
geom_line(linewidth = 1) +
labs(
title = "Home-Away Difference Over Total Minutes",
x = "Total Minutes",
y = "Home-Away Difference",
color = "Category"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = "bottom"
)
bad_category_data <- last_training_data %>%
filter(category == "Bad")
ggplot(bad_category_data, aes(x = total_minute, y = home_away_diff, group = fixture_id, color = as.factor(fixture_id))) +
geom_line(size = 1) +
labs(
title = "Home-Away Difference Over Total Minutes (Category: Bad)",
x = "Total Minutes",
y = "Home-Away Difference",
color = "Match ID"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = "none"
)## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
set.seed(123)
random_fixture_ids <- sample(unique(bad_category_data$fixture_id), 50)
random_sample_data <- bad_category_data %>%
filter(fixture_id %in% random_fixture_ids)
ggplot(random_sample_data, aes(x = total_minute, y = home_away_diff, group = fixture_id, color = as.factor(fixture_id))) +
geom_line(size = 1) +
labs(
title = "Home-Away Difference Over Total Minutes (Random 50 Matches, Category: Bad)",
x = "Total Minutes",
y = "Home-Away Difference",
color = "Match ID"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = "none"
)
std_dev_per_minute <- bad_category_data %>%
group_by(total_minute) %>%
summarise(std_dev = sd(home_away_diff, na.rm = TRUE))
average_std_dev <- mean(std_dev_per_minute$std_dev, na.rm = TRUE)
print(average_std_dev)## [1] 0.2791264print(std_dev_per_minute)## # A tibble: 103 × 2
## total_minute std_dev
## <dbl> <dbl>
## 1 0 0.112
## 2 1 0.123
## 3 2 0.124
## 4 3 0.133
## 5 4 0.134
## 6 5 0.144
## 7 6 0.158
## 8 7 0.160
## 9 8 0.167
## 10 9 0.172
## # ℹ 93 more rowslibrary(qcc)## Package 'qcc' version 2.7## Type 'citation("qcc")' for citing this R package in publications.std_dev_per_minute <- std_dev_per_minute %>%
mutate(std_dev_diff = std_dev - lag(std_dev)) %>%
filter(!is.na(std_dev_diff))
xbar_data <- std_dev_per_minute$std_dev_diff
custom_sigma <- sd(xbar_data, na.rm = TRUE) * 0.25
xbar_chart <- qcc(data = xbar_data,
type = "xbar.one",
std.dev = custom_sigma,
title = "X-bar Chart for Std Dev Differences (Reduced Sigma)",
xlab = "Minutes",
ylab = "Std Dev Difference")
cusum_chart <- cusum(xbar_data,decision.interval = 4, se.shift = 0.25)
good_category_data <- last_training_data %>%
filter(category == "Good")
ggplot(good_category_data, aes(x = total_minute, y = home_away_diff, group = fixture_id, color = as.factor(fixture_id))) +
geom_line(size = 1) +
labs(
title = "Home-Away Difference Over Total Minutes (Category: Good)",
x = "Total Minutes",
y = "Home-Away Difference",
color = "Match ID"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = "none"
)
set.seed(123)
random_fixture_ids_good <- sample(unique(good_category_data$fixture_id), 50)
random_sample_data_good <- good_category_data %>%
filter(fixture_id %in% random_fixture_ids)
ggplot(random_sample_data_good, aes(x = total_minute, y = home_away_diff, group = fixture_id, color = as.factor(fixture_id))) +
geom_line(size = 1) +
labs(
title = "Home-Away Difference Over Total Minutes (Random 50 Matches, Category: Good)",
x = "Total Minutes",
y = "Home-Away Difference",
color = "Match ID"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = "none"
)
std_dev_per_minute_good <- good_category_data %>%
group_by(total_minute) %>%
summarise(std_dev = sd(home_away_diff, na.rm = TRUE))
average_std_dev_good <- mean(std_dev_per_minute_good$std_dev, na.rm = TRUE)
print(average_std_dev_good)## [1] 0.2704378print(std_dev_per_minute_good)## # A tibble: 116 × 2
## total_minute std_dev
## <dbl> <dbl>
## 1 0 0.0471
## 2 1 0.0482
## 3 2 0.0481
## 4 3 0.0655
## 5 4 0.0816
## 6 5 0.0945
## 7 6 0.107
## 8 7 0.124
## 9 8 0.141
## 10 9 0.147
## # ℹ 106 more rowsstd_dev_per_minute_good <- std_dev_per_minute_good %>%
mutate(std_dev_diff = std_dev - lag(std_dev)) %>%
filter(!is.na(std_dev_diff))
xbar_data_good <- std_dev_per_minute_good$std_dev_diff
custom_sigma_good <- sd(xbar_data_good, na.rm = TRUE) * 0.25
xbar_chart_good <- qcc(data = xbar_data_good,
type = "xbar.one",
std.dev = custom_sigma_good,
title = "X-bar Chart for Std Dev Differences (Reduced Sigma)",
xlab = "Minutes",
ylab = "Std Dev Difference")
cusum_chart <- cusum(xbar_data_good,decision.interval = 4, se.shift = 1)
medium_category_data <- last_training_data %>%
filter(category == "Medium")
ggplot(medium_category_data, aes(x = total_minute, y = home_away_diff, group = fixture_id, color = as.factor(fixture_id))) +
geom_line(size = 1) +
labs(
title = "Home-Away Difference Over Total Minutes (Category: Medium)",
x = "Total Minutes",
y = "Home-Away Difference",
color = "Match ID"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = "none"
)
set.seed(123)
random_fixture_ids_medium <- sample(unique(medium_category_data$fixture_id), 50)
random_sample_data_medium <- medium_category_data %>%
filter(fixture_id %in% random_fixture_ids_medium)
ggplot(random_sample_data_medium, aes(x = total_minute, y = home_away_diff, group = fixture_id, color = as.factor(fixture_id))) +
geom_line(size = 1) +
labs(
title = "Home-Away Difference Over Total Minutes (Random 50 Matches, Category: Medium)",
x = "Total Minutes",
y = "Home-Away Difference",
color = "Match ID"
) +
theme_minimal() +
theme(
plot.title = element_text(hjust = 0.5),
legend.position = "none"
)
std_dev_per_minute_medium <- medium_category_data %>%
group_by(total_minute) %>%
summarise(std_dev = sd(home_away_diff, na.rm = TRUE))
average_std_dev_medium <- mean(std_dev_per_minute_medium$std_dev, na.rm = TRUE)
print(average_std_dev_medium)## [1] 0.2618393print(std_dev_per_minute_medium)## # A tibble: 100 × 2
## total_minute std_dev
## <dbl> <dbl>
## 1 0 0.0613
## 2 1 0.0597
## 3 2 0.0592
## 4 3 0.0673
## 5 4 0.0790
## 6 5 0.0772
## 7 6 0.100
## 8 7 0.101
## 9 8 0.124
## 10 9 0.128
## # ℹ 90 more rowsstd_dev_per_minute_medium <- std_dev_per_minute_medium %>%
mutate(std_dev_diff = std_dev - lag(std_dev)) %>%
filter(!is.na(std_dev_diff))
xbar_data_medium <- std_dev_per_minute_medium$std_dev_diff
custom_sigma_medium <- sd(xbar_data_medium, na.rm = TRUE) * 0.25
xbar_chart_medium <- qcc(data = xbar_data_medium,
type = "xbar.one",
std.dev = custom_sigma_medium,
title = "X-bar Chart for Std Dev Differences (Reduced Sigma)",
xlab = "Minutes",
ylab = "Std Dev Difference")
cusum_chart_medium <- cusum(xbar_data_medium,decision.interval = 4, se.shift = 1)
grouped_data_bad <- std_dev_per_minute %>%
mutate(group = floor(total_minute / 3)) %>%
group_by(group) %>%
summarise(mean_diff = mean(std_dev_diff, na.rm = TRUE))
xbar_data_grouped_bad <- grouped_data_bad$mean_diff
cusum_chart_bad <- cusum(xbar_data_grouped_bad,decision.interval = 4, se.shift = 1)
xbar_chart_bad <- qcc(data = xbar_data_grouped_bad,
type = "xbar.one",
title = "X-bar Chart for Std Dev Differences (Grouped Data)",
xlab = "3-minute Intervals",
ylab = "Mean Std Dev Difference")
grouped_data_good <- std_dev_per_minute_good %>%
mutate(group = floor(total_minute / 3)) %>%
group_by(group) %>%
summarise(mean_diff = mean(std_dev_diff, na.rm = TRUE))
xbar_data_grouped_good <- grouped_data_good$mean_diff
cusum_chart_good <- cusum(xbar_data_grouped_good,decision.interval = 4, se.shift = 1)
xbar_chart_good <- qcc(data = xbar_data_grouped_good,
type = "xbar.one",
title = "X-bar Chart for Std Dev Differences (Grouped Data)",
xlab = "3-minute Intervals",
ylab = "Mean Std Dev Difference")
grouped_data_medium <- std_dev_per_minute_medium %>%
mutate(group = floor(total_minute / 3)) %>%
group_by(group) %>%
summarise(mean_diff = mean(std_dev_diff, na.rm = TRUE))
xbar_data_grouped_medium <- grouped_data_medium$mean_diff
cusum_chart_medium <- cusum(xbar_data_grouped_medium,decision.interval = 4, se.shift = 1)
xbar_chart_medium <- qcc(data = xbar_data_grouped_medium,
type = "xbar.one",
title = "X-bar Chart for Std Dev Differences (Grouped Data)",
xlab = "3-minute Intervals",
ylab = "Mean Std Dev Difference")
Base model: DT
last_training_data <- last_training_data[, !colnames(last_training_data) %in% c("fixture_id")]
predictors <- last_training_data
target <- last_training_data$result
formula <- result ~ .
rf_train_data <- data.frame(predictors, result = target)
train_control <- trainControl(method = "cv", number = 4)
# Set hyperparameters for tuning
tune_grid <- expand.grid(cp = 0.08) # Complexity parameter
# Train the model using rpart
rpart_model <- train(
formula,
data = rf_train_data,
method = "rpart",
trControl = train_control,
tuneGrid = tune_grid
)
# Display the best model
print(rpart_model$bestTune)## cp
## 1 0.08conf_matrix <- confusionMatrix(tree_model_predictions, initial_test_data$result)
print(conf_matrix)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 935 1220 504
## 1 566 2967 419
## 2 718 697 1810
##
## Overall Statistics
##
## Accuracy : 0.5807
## 95% CI : (0.5709, 0.5905)
## No Information Rate : 0.4965
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.3534
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.42136 0.6075 0.6623
## Specificity 0.77366 0.8011 0.8008
## Pos Pred Value 0.35164 0.7508 0.5612
## Neg Pred Value 0.82110 0.6742 0.8604
## Prevalence 0.22560 0.4965 0.2779
## Detection Rate 0.09506 0.3016 0.1840
## Detection Prevalence 0.27033 0.4018 0.3279
## Balanced Accuracy 0.59751 0.7043 0.7315# Print only the accuracy
cat("Decision Tree Accuracy:", conf_matrix$overall["Accuracy"], "\n")## Decision Tree Accuracy: 0.5807239# Plot the model performance
#plot(rpart_model)Select complexity parameter as 0.08 as a result of analysis.
# Set seed for reproducibility
set.seed(123)
last_training_data <- last_training_data[, !colnames(last_training_data) %in% c("fixture_id")]
predictors <- last_training_data[, !colnames(last_training_data) %in% c("result")]
target <- last_training_data$result
# Create a data frame for caret
rf_train_data <- data.frame(predictors, target)
# Define the training control with 10-fold cross-validation
train_control <- trainControl(method = "cv", number = 4)
#COMBINE TUNE GRIDS!!!
# Define the grid for mtry and cp
tune_grid <- expand.grid(
mtry = c(3)
)
# Custom Random Forest model wrapper for caret
custom_rf <- list(
type = "Classification",
library = "randomForest",
loop = NULL,
parameters = data.frame(
parameter = c("mtry"),
class = c("numeric"),
label = c("mtry")
),
grid = function(x, y, len = NULL, search = "grid") {
expand.grid(
mtry = seq(2, ncol(x), length.out = len),
cp = seq(0.01, 0.1, length.out = len)
)
},
fit = function(x, y, wts, param, lev, last, weights, classProbs, ...) {
randomForest(x = x, y = y, mtry = param$mtry, ntree = 300, maxnodes = 10, ...)
},
predict = function(modelFit, newdata, submodels = NULL) {
predict(modelFit, newdata)
},
prob = function(modelFit, newdata, submodels = NULL) {
predict(modelFit, newdata, type = "prob")
},
varImp = function(object, ...) {
varImp(object, ...)
}
)
rf_train_data$target <- as.factor(rf_train_data$target)
# Fit the Random Forest model with caret
rf_model <- train(
target ~ .,
data = rf_train_data,
method = custom_rf,
trControl = train_control,
tuneGrid = tune_grid
)
# Look at all the results (including Accuracy, Kappa, etc.)
print(rf_model$results)## mtry Accuracy Kappa AccuracySD KappaSD
## 1 3 0.6378563 0.4292862 0.003735592 0.006605241# Extract the accuracy specifically for the best mtry
best_mtry <- rf_model$bestTune$mtry
best_row <- rf_model$results$mtry == best_mtry
best_accuracy <- rf_model$results$Accuracy[best_row]
cat("Cross-validated Accuracy:", best_accuracy, "\n")## Cross-validated Accuracy: 0.6378563# Display the best model parameters
print(rf_model$bestTune)## mtry
## 1 3final_rf_model <- rf_model$finalModel
print(final_rf_model)##
## Call:
## randomForest(x = x, y = y, ntree = 300, mtry = param$mtry, maxnodes = 10)
## Type of random forest: classification
## Number of trees: 300
## No. of variables tried at each split: 3
##
## OOB estimate of error rate: 36.71%
## Confusion matrix:
## 0 1 2 class.error
## 0 2870 6990 3312 0.7821136
## 1 704 16996 1564 0.1177326
## 2 653 3771 9431 0.3193071last_test_data <- cleaned_data[cleaned_data$fixture_id %in% test_list, ]
last_test_data <- last_test_data[, !colnames(last_test_data)%in%c("fixture_id")]
last_training_data <- last_training_data[, !colnames(last_training_data)%in%c("fixture_id")]#```{r} set.seed(123)
tune_out <- e1071::tune( METHOD= svm, train.x = result ~ ., data = last_training_data, kernel = “radial”, ranges = list(cost = c(0.1, 1, 10), gamma = c(0.01, 0.1, 1)) )
Print the best parameters
print(tune_out$best.parameters)
Train an SVM model with the best parameters from tuning
best_cost <- tune_out\(best.parameters\)cost best_gamma <- tune_out\(best.parameters\)gamma
svm_model <- svm( result ~ ., data = last_training_data, kernel = “radial”, cost = best_cost, gamma = best_gamma, probability=TRUE )
Make predictions on the test data
svm_predictions <- predict(svm_model, newdata = cleaned_test_data, probability=TRUE)
Evaluate the model using confusion matrix
conf_matrix_svm <- confusionMatrix(svm_predictions, cleaned_test_data$result)
Print SVM accuracy
print(“SVM Accuracy:”) print(conf_matrix_svm$overall[“Accuracy”])
#```{r}
selected_features <- importance_df[1:10, "Feature"]
reduced_training_data <- last_training_data[, c(selected_features, "result")]
reduced_test_data <- last_test_data[, c(selected_features, "result")]
set.seed(120)
tune_out <- e1071::tune(
METHOD = svm,
result ~ .,
data = reduced_training_data,
kernel = "radial",
#ranges = list(cost = c(0.1, 1, 10), gamma = c(0.01, 0.1, 1))
ranges = list(cost = c(1), gamma = c(0.1))
)
print(tune_out$best.parameters)
# Train the final SVM model with the best parameters
best_cost <- tune_out$best.parameters$cost
best_gamma <- tune_out$best.parameters$gamma
svm_model <- svm(
result ~ .,
data = reduced_training_data,
kernel = "radial",
cost = best_cost,
gamma = best_gamma
)
# Make predictions on the test data
svm_predictions <- predict(svm_model, newdata = reduced_test_data)
# Evaluate the model using confusion matrix
conf_matrix_svm <- confusionMatrix(svm_predictions, reduced_test_data$result)
# Print SVM accuracy
print("SVM Accuracy:")
print(conf_matrix_svm$overall["Accuracy"])library(nnet)
last_training_data$result <- as.factor(last_training_data$result)
multinom_model <- multinom(result ~ ., data = last_training_data)## # weights: 339 (224 variable)
## initial value 50855.861455
## iter 10 value 42456.827702
## iter 20 value 41225.702194
## iter 30 value 39896.334642
## iter 40 value 38524.438389
## iter 50 value 37502.989771
## iter 60 value 37002.417099
## iter 70 value 36841.945907
## iter 80 value 36755.930194
## iter 90 value 36699.650971
## iter 100 value 36566.821951
## final value 36566.821951
## stopped after 100 iterationssummary(multinom_model)## Call:
## multinom(formula = result ~ ., data = last_training_data)
##
## Coefficients:
## (Intercept) halftime X1 X2 X
## 1 0.06542639 -0.04170214 -0.0008811334 0.003459303 -0.001191443
## 2 -0.08008689 -0.08939567 -0.0047763126 -0.002097327 0.025911908
## Accurate.Crosses...away Accurate.Crosses...home Assists...away Assists...home
## 1 0.02958789 -0.01846742 -0.6847950 -0.07306789
## 2 0.01468825 0.04599895 -0.3834915 -0.02504639
## Attacks...away Attacks...home Ball.Possession.....away
## 1 -0.006591071 0.00722411 0.002122945
## 2 -0.010410493 -0.01286382 -0.017370105
## Ball.Possession.....home Ball.Safe...away Ball.Safe...home Challenges...away
## 1 -0.008245471 -0.02732779 0.011255108 -0.09390845
## 2 -0.012092699 -0.01809570 0.007670896 0.04664301
## Challenges...home Corners...away Corners...home Counter.Attacks...away
## 1 -0.2203196 -0.04952614 0.03769567 0.2019885
## 2 -0.1067866 -0.06316117 0.14342512 0.2491050
## Counter.Attacks...home Dangerous.Attacks...away Dangerous.Attacks...home
## 1 -0.2201226 0.0189742608 0.01467896
## 2 -0.1145961 -0.0009648976 0.03194152
## Dribble.Attempts...away Dribble.Attempts...home Fouls...away Fouls...home
## 1 0.006588047 0.03963839 -0.01137214 -0.05363000
## 2 0.012292581 0.04493672 0.01342943 -0.00529716
## Free.Kicks...away Free.Kicks...home Goal.Attempts...away Goal.Attempts...home
## 1 -0.10605705 0.06552679 -0.091439700 0.070997860
## 2 0.01785479 -0.08987409 0.006384703 0.004053885
## Goal.Kicks...away Goal.Kicks...home Goals...away Goals...home Headers...away
## 1 -0.001326814 0.009601596 0.5245672 -0.05608746 0.10443283
## 2 -0.027345146 0.024786608 0.1732640 -0.17099495 0.05776244
## Headers...home Hit.Woodwork...away Hit.Woodwork...home Injuries...away
## 1 0.04069853 0.1353993 -0.121878166 0.15485236
## 2 0.02846394 0.5357512 0.005877538 -0.06257897
## Injuries...home Interceptions...away Interceptions...home Key.Passes...away
## 1 0.1877494 0.03321738 0.14575267 -0.074517799
## 2 0.3182627 -0.11049967 0.05314849 -0.004833966
## Key.Passes...home Long.Passes...away Long.Passes...home Offsides...away
## 1 0.089540334 -0.015493114 0.01361541 -0.08840556
## 2 0.003420427 0.007804662 0.01498631 -0.05570284
## Offsides...home Passes...away Passes...home Penalties...away Penalties...home
## 1 0.03467218 -0.010156644 0.02286888 -0.01077974 0.4035265
## 2 0.04754343 -0.006084897 0.01610277 0.07121096 0.2033502
## Redcards...away Redcards...home Saves...away Saves...home
## 1 -0.1085147 -0.1249062 -0.020213194 -0.3338354
## 2 0.1776220 -0.4391250 0.003101876 -0.1323672
## Shots.Blocked...away Shots.Blocked...home Shots.Insidebox...away
## 1 0.04481439 -0.01448913 0.03580814
## 2 0.41041888 -0.02177946 0.06458782
## Shots.Insidebox...home Shots.Off.Target...away Shots.Off.Target...home
## 1 -0.13230727 0.2454050 0.06029353
## 2 0.02804451 0.4182552 0.09529720
## Shots.On.Target...away Shots.On.Target...home Shots.Outsidebox...away
## 1 0.5154095 -0.050679102 0.09662105
## 2 0.5510295 0.008839872 0.09105393
## Shots.Outsidebox...home Shots.Total...away Shots.Total...home
## 1 -0.158617452 -0.1577871 0.06574961
## 2 -0.001671689 -0.5045325 -0.06256009
## Substitutions...away Substitutions...home Successful.Dribbles...away
## 1 -0.07615296 0.094306668 -0.02314751
## 2 -0.01916510 -0.005357125 -0.04320119
## Successful.Dribbles...home Successful.Headers...away
## 1 0.03880997 -0.15614102
## 2 -0.00597419 -0.06675273
## Successful.Headers...home Successful.Interceptions...away
## 1 -0.13052246 -0.006641746
## 2 -0.09132428 0.012544500
## Successful.Interceptions...home Successful.Passes...away
## 1 -0.029686162 0.015967755
## 2 0.004086644 0.006003648
## Successful.Passes...home Successful.Passes.Percentage...away
## 1 -0.03035361 -0.007923756
## 2 -0.02194662 0.016015708
## Successful.Passes.Percentage...home Tackles...away Tackles...home
## 1 0.003027573 0.006283671 0.019241731
## 2 0.001988007 -0.034856365 0.002545399
## Throwins...away Throwins...home Total.Crosses...away Total.Crosses...home
## 1 0.012589093 0.02048759 -0.01028400 -0.03019807
## 2 -0.004981377 0.03323831 0.01262018 -0.09665400
## Yellowcards...away Yellowcards...home Yellowred.Cards...away
## 1 0.03787504 0.04886104 -1.251065
## 2 0.06159102 0.12632927 1.534482
## Yellowred.Cards...home current_state P_home P_draw P_away
## 1 -0.3945888 -0.05111244 2.0559550 -1.717554 -0.2928894
## 2 -1.3043955 -0.17704624 -0.2330915 -1.105501 1.2918841
## total_prob P_home_norm P_draw_norm P_away_norm total_minute goal_difference
## 1 0.04551162 1.964862 -1.606007 -0.2934279 -0.017525559 -0.5806547
## 2 -0.04670803 -0.272802 -1.038532 1.2312466 0.001730969 -0.3442589
## yellow_card_difference goal_elapsed_interaction
## 1 0.01098600 0.002176322
## 2 0.06473825 0.011885397
## goal_yellowcards_home_interaction goal_yellowcards_away_interaction
## 1 -0.06228822 0.05989207
## 2 -0.02345266 0.01091436
## attack_efficiency_home interaction_passes_attacks_home
## 1 -0.020848280 4.335526e-05
## 2 -0.001648534 4.116764e-05
## interaction_passes_attacks_away attack_efficiency_away categoryGood
## 1 2.605854e-06 0.004741539 0.4268476
## 2 1.451398e-05 0.007742683 0.7422254
## categoryMedium home_away_diff
## 1 0.0555911 0.2071055
## 2 0.4140867 1.0267934
##
## Std. Errors:
## (Intercept) halftime X1 X2 X
## 1 2.242647e-05 3.221842e-05 0.0004317021 0.0005171154 0.001477987
## 2 2.586135e-05 3.583795e-05 0.0003630103 0.0006087936 0.001412426
## Accurate.Crosses...away Accurate.Crosses...home Assists...away Assists...home
## 1 0.0003131678 0.0003927529 6.430092e-05 7.718931e-05
## 2 0.0003472164 0.0003685376 6.521461e-05 6.940800e-05
## Attacks...away Attacks...home Ball.Possession.....away
## 1 0.001969151 0.001755895 0.001483519
## 2 0.001930075 0.001829913 0.001608464
## Ball.Possession.....home Ball.Safe...away Ball.Safe...home Challenges...away
## 1 0.001626007 0.001314298 0.001327265 0.0009391584
## 2 0.001751438 0.001325163 0.001342485 0.0009167956
## Challenges...home Corners...away Corners...home Counter.Attacks...away
## 1 0.001058330 0.0003232450 0.0003647388 0.0000966170
## 2 0.001162182 0.0003407634 0.0003438681 0.0001267702
## Counter.Attacks...home Dangerous.Attacks...away Dangerous.Attacks...home
## 1 9.211727e-05 0.001636270 0.001523421
## 2 1.081049e-04 0.001628061 0.001508570
## Dribble.Attempts...away Dribble.Attempts...home Fouls...away Fouls...home
## 1 0.0008257489 0.001046604 0.0007447405 0.0005008488
## 2 0.0009320374 0.001140982 0.0007533900 0.0005490676
## Free.Kicks...away Free.Kicks...home Goal.Attempts...away Goal.Attempts...home
## 1 0.0005779950 0.0005760415 0.0002810160 0.0003340833
## 2 0.0007656605 0.0006920269 0.0003152607 0.0003214110
## Goal.Kicks...away Goal.Kicks...home Goals...away Goals...home Headers...away
## 1 0.0003379881 0.0003688092 8.787419e-05 9.383499e-05 0.001410640
## 2 0.0003486578 0.0004049695 8.314383e-05 8.369658e-05 0.001478094
## Headers...home Hit.Woodwork...away Hit.Woodwork...home Injuries...away
## 1 0.001387668 3.719687e-05 3.873359e-05 4.984556e-05
## 2 0.001443695 4.049607e-05 4.042760e-05 4.666951e-05
## Injuries...home Interceptions...away Interceptions...home Key.Passes...away
## 1 5.359628e-05 0.0009366516 0.001062822 0.0007833982
## 2 5.813566e-05 0.0009139562 0.001165768 0.0008583835
## Key.Passes...home Long.Passes...away Long.Passes...home Offsides...away
## 1 0.0008134533 0.001652017 0.001724941 9.123923e-05
## 2 0.0007729358 0.001773151 0.001668663 9.549563e-05
## Offsides...home Passes...away Passes...home Penalties...away Penalties...home
## 1 0.0001171837 0.001137818 0.0009844657 2.650638e-05 3.008213e-05
## 2 0.0001231050 0.001077027 0.0010713305 2.925425e-05 2.665410e-05
## Redcards...away Redcards...home Saves...away Saves...home
## 1 1.250545e-05 1.461054e-05 0.0003350068 0.0002569588
## 2 1.460858e-05 1.388398e-05 0.0003175995 0.0002892885
## Shots.Blocked...away Shots.Blocked...home Shots.Insidebox...away
## 1 0.0003045223 0.0003087673 0.0006426482
## 2 0.0003320126 0.0002747468 0.0007227259
## Shots.Insidebox...home Shots.Off.Target...away Shots.Off.Target...home
## 1 0.0008017255 0.0004483438 0.0004262465
## 2 0.0007504083 0.0004827154 0.0004186094
## Shots.On.Target...away Shots.On.Target...home Shots.Outsidebox...away
## 1 0.0002901863 0.0003776826 0.0003460086
## 2 0.0003178006 0.0003538911 0.0003712566
## Shots.Outsidebox...home Shots.Total...away Shots.Total...home
## 1 0.0002528798 0.0009891557 0.0010260937
## 2 0.0002486071 0.0010833553 0.0009700368
## Substitutions...away Substitutions...home Successful.Dribbles...away
## 1 0.0001852304 0.0001669612 0.0003474847
## 2 0.0001989544 0.0001687251 0.0003932869
## Successful.Dribbles...home Successful.Headers...away
## 1 0.0004654982 0.0007612375
## 2 0.0004870804 0.0008149585
## Successful.Headers...home Successful.Interceptions...away
## 1 0.0007351805 0.0009076735
## 2 0.0007879022 0.0009124733
## Successful.Interceptions...home Successful.Passes...away
## 1 0.0008946641 0.001208624
## 2 0.0009342259 0.001150041
## Successful.Passes...home Successful.Passes.Percentage...away
## 1 0.001012292 0.001434557
## 2 0.001112334 0.001522433
## Successful.Passes.Percentage...home Tackles...away Tackles...home
## 1 0.001566904 0.0009071307 0.0009889907
## 2 0.001595124 0.0010168504 0.0010740137
## Throwins...away Throwins...home Total.Crosses...away Total.Crosses...home
## 1 0.001076338 0.001558823 0.0007300906 0.001166819
## 2 0.001063312 0.001677347 0.0008029667 0.001059204
## Yellowcards...away Yellowcards...home Yellowred.Cards...away
## 1 0.0001668271 0.0001060338 2.712302e-06
## 2 0.0001648543 0.0001132662 4.822117e-06
## Yellowred.Cards...home current_state P_home P_draw P_away
## 1 3.873690e-06 5.833656e-05 1.920956e-05 1.928583e-05 1.850434e-05
## 2 4.418994e-06 7.726058e-05 2.209892e-05 2.730926e-05 2.178531e-05
## total_prob P_home_norm P_draw_norm P_away_norm total_minute
## 1 2.370430e-05 1.817066e-05 1.808035e-05 1.753819e-05 0.001633907
## 2 2.730867e-05 2.092872e-05 2.558989e-05 2.064816e-05 0.001613225
## goal_difference yellow_card_difference goal_elapsed_interaction
## 1 3.217599e-05 0.0001424774 0.0003863024
## 2 2.747392e-05 0.0001432483 0.0003880649
## goal_yellowcards_home_interaction goal_yellowcards_away_interaction
## 1 8.895594e-05 7.657147e-05
## 2 1.013849e-04 7.060053e-05
## attack_efficiency_home interaction_passes_attacks_home
## 1 0.001346882 3.598699e-06
## 2 0.001432395 3.722370e-06
## interaction_passes_attacks_away attack_efficiency_away categoryGood
## 1 4.187984e-06 0.001406946 4.077143e-05
## 2 4.056467e-06 0.001419143 4.845101e-05
## categoryMedium home_away_diff
## 1 4.273182e-05 3.259427e-05
## 2 4.467950e-05 4.141557e-05
##
## Residual Deviance: 73133.64
## AIC: 73565.64predicted_probs <- predict(multinom_model, newdata = last_training_data, type = "probs")
predicted_classes <- predict(multinom_model, newdata = last_training_data, type = "class")
conf_matrix <- confusionMatrix(predicted_classes, last_training_data$result)
print("Multinomial Logistic Regression Accuracy:")## [1] "Multinomial Logistic Regression Accuracy:"print(conf_matrix$overall["Accuracy"])## Accuracy
## 0.6557646good_test_data <- last_test_data[last_test_data$category == "Good", ]
medium_test_data <- last_test_data[last_test_data$category == "Medium", ]
bad_test_data <- last_test_data[last_test_data$category == "Bad", ]
good_category_data <- good_category_data[, !colnames(good_category_data)%in%c("fixture_id")]
medium_category_data <- medium_category_data[, !colnames(medium_category_data)%in%c("fixture_id")]
bad_category_data <- bad_category_data[, !colnames(bad_category_data)%in%c("fixture_id")]
good_category_data$category <- NULL
medium_category_data$category <- NULL
bad_category_data$category <- NULL
good_test_data$category <- NULL
medium_test_data$category <- NULL
bad_test_data$category <- NULLlibrary(xgboost)
#good
good_target <- as.numeric(as.character(good_category_data$result))
good_features <- good_category_data[, !names(good_category_data) %in% "result"]
good_matrix <- xgb.DMatrix(data = as.matrix(good_features), label = good_target)
params <- list(
objective = "multi:softmax",
num_class = 3,
eval_metric = "merror",
eta = 0.05,
max_depth = 3,
nthread = 2
)
num_round <- 100
model_good <- xgb.train(
params = params,
data = good_matrix,
nrounds = num_round
)
#testing
preds_good <- predict(model_good, good_matrix)
conf_matrix_good <- confusionMatrix(as.factor(preds_good), as.factor(good_target))
cat("\n-- Good Category --\n")##
## -- Good Category --print(conf_matrix_good)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 2979 305 215
## 1 832 4165 565
## 2 630 888 4821
##
## Overall Statistics
##
## Accuracy : 0.7769
## 95% CI : (0.7703, 0.7835)
## No Information Rate : 0.3637
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.6616
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.6708 0.7773 0.8607
## Specificity 0.9526 0.8609 0.8451
## Pos Pred Value 0.8514 0.7488 0.7605
## Neg Pred Value 0.8772 0.8787 0.9139
## Prevalence 0.2884 0.3479 0.3637
## Detection Rate 0.1934 0.2705 0.3131
## Detection Prevalence 0.2272 0.3612 0.4116
## Balanced Accuracy 0.8117 0.8191 0.8529good_test_target <- good_test_data$result
good_test_features <- good_test_data[, !names(good_test_data) %in% "result"]
good_test_matrix <- xgb.DMatrix(data = as.matrix(good_test_features))
preds_good_test <- predict(model_good, good_test_matrix)
conf_matrix_good_test <- confusionMatrix(
as.factor(preds_good_test),
as.factor(good_test_target)
)
cat("\n-- Good Category TEST --\n")##
## -- Good Category TEST --print(conf_matrix_good_test)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 299 295 99
## 1 414 916 153
## 2 500 314 781
##
## Overall Statistics
##
## Accuracy : 0.5293
## 95% CI : (0.5132, 0.5453)
## No Information Rate : 0.4044
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.2932
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.24650 0.6007 0.7561
## Specificity 0.84597 0.7476 0.7027
## Pos Pred Value 0.43146 0.6177 0.4897
## Neg Pred Value 0.70305 0.7338 0.8842
## Prevalence 0.32167 0.4044 0.2739
## Detection Rate 0.07929 0.2429 0.2071
## Detection Prevalence 0.18377 0.3933 0.4230
## Balanced Accuracy 0.54623 0.6741 0.7294medium_target <- as.numeric(as.character(medium_category_data$result))
medium_features <- medium_category_data[, !names(medium_category_data) %in% "result"]
medium_matrix <- xgb.DMatrix(data = as.matrix(medium_features), label = medium_target)
params <- list(
objective = "multi:softmax",
num_class = 3,
eval_metric = "merror",
eta = 0.05,
max_depth = 3,
nthread = 2
)
num_round <- 100
model_medium <- xgb.train(
params = params,
data = medium_matrix,
nrounds = num_round
)
#testing
preds_medium <- predict(model_medium, medium_matrix)
conf_matrix_medium <- confusionMatrix(as.factor(preds_medium), as.factor(medium_target))
cat("\n-- medium Category --\n")##
## -- medium Category --print(conf_matrix_medium)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 3613 421 319
## 1 828 4814 532
## 2 677 487 4281
##
## Overall Statistics
##
## Accuracy : 0.7956
## 95% CI : (0.7893, 0.8019)
## No Information Rate : 0.3583
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.6925
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.7059 0.8413 0.8342
## Specificity 0.9318 0.8673 0.8926
## Pos Pred Value 0.8300 0.7797 0.7862
## Neg Pred Value 0.8705 0.9073 0.9192
## Prevalence 0.3204 0.3583 0.3213
## Detection Rate 0.2262 0.3014 0.2680
## Detection Prevalence 0.2725 0.3866 0.3409
## Balanced Accuracy 0.8189 0.8543 0.8634medium_test_target <- medium_test_data$result
medium_test_features <- medium_test_data[, !names(medium_test_data) %in% "result"]
medium_test_matrix <- xgb.DMatrix(data = as.matrix(medium_test_features))
preds_medium_test <- predict(model_medium, medium_test_matrix)
conf_matrix_medium_test <- confusionMatrix(
as.factor(preds_medium_test),
as.factor(medium_test_target)
)
cat("\n-- medium Category TEST --\n")##
## -- medium Category TEST --print(conf_matrix_medium_test)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 200 398 172
## 1 225 588 211
## 2 212 288 721
##
## Overall Statistics
##
## Accuracy : 0.5005
## 95% CI : (0.4825, 0.5185)
## No Information Rate : 0.4226
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.2365
##
## Mcnemar's Test P-Value : 7.858e-14
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.31397 0.4615 0.6531
## Specificity 0.76030 0.7496 0.7384
## Pos Pred Value 0.25974 0.5742 0.5905
## Neg Pred Value 0.80535 0.6554 0.7865
## Prevalence 0.21128 0.4226 0.3662
## Detection Rate 0.06633 0.1950 0.2391
## Detection Prevalence 0.25539 0.3396 0.4050
## Balanced Accuracy 0.53714 0.6056 0.6957bad_target <- as.numeric(as.character(bad_category_data$result))
bad_features <- bad_category_data[, !names(bad_category_data) %in% "result"]
bad_matrix <- xgb.DMatrix(data = as.matrix(bad_features), label = bad_target)
params <- list(
objective = "multi:softmax",
num_class = 3,
eval_metric = "merror",
eta = 0.05,
max_depth = 3,
nthread = 2
)
num_round <- 100
model_bad <- xgb.train(
params = params,
data = bad_matrix,
nrounds = num_round
)
#testing
preds_bad <- predict(model_bad, bad_matrix)
conf_matrix_bad <- confusionMatrix(as.factor(preds_bad), as.factor(bad_target))
cat("\n-- bad Category --\n")##
## -- bad Category --print(conf_matrix_bad)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 2061 43 126
## 1 1331 8058 467
## 2 221 83 2529
##
## Overall Statistics
##
## Accuracy : 0.8478
## 95% CI : (0.8419, 0.8535)
## No Information Rate : 0.5486
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.729
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.5704 0.9846 0.8101
## Specificity 0.9851 0.7330 0.9742
## Pos Pred Value 0.9242 0.8176 0.8927
## Neg Pred Value 0.8777 0.9751 0.9509
## Prevalence 0.2422 0.5486 0.2093
## Detection Rate 0.1381 0.5401 0.1695
## Detection Prevalence 0.1495 0.6606 0.1899
## Balanced Accuracy 0.7777 0.8588 0.8921bad_test_target <- bad_test_data$result
bad_test_features <- bad_test_data[, !names(bad_test_data) %in% "result"]
bad_test_matrix <- xgb.DMatrix(data = as.matrix(bad_test_features))
preds_bad_test <- predict(model_bad, bad_test_matrix)
conf_matrix_bad_test <- confusionMatrix(
as.factor(preds_bad_test),
as.factor(bad_test_target)
)
cat("\n-- bad Category TEST --\n")##
## -- bad Category TEST --print(conf_matrix_bad_test)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 136 100 144
## 1 139 1965 180
## 2 94 20 272
##
## Overall Statistics
##
## Accuracy : 0.778
## 95% CI : (0.7629, 0.7927)
## No Information Rate : 0.6836
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5048
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.36856 0.9424 0.45638
## Specificity 0.90899 0.6694 0.95355
## Pos Pred Value 0.35789 0.8603 0.70466
## Neg Pred Value 0.91273 0.8433 0.87838
## Prevalence 0.12098 0.6836 0.19541
## Detection Rate 0.04459 0.6443 0.08918
## Detection Prevalence 0.12459 0.7489 0.12656
## Balanced Accuracy 0.63878 0.8059 0.70496good_test_data2 <- last_test_data[last_test_data$category == "Good", ]
medium_test_data2 <- last_test_data[last_test_data$category == "Medium", ]
bad_test_data2 <- last_test_data[last_test_data$category == "Bad", ]filter_by_minute <- function(data, prediction_minute) {
data %>% filter(total_minute == prediction_minute)
}
good_test_data_filtered <- filter_by_minute(good_test_data2, 36)
medium_test_data_filtered <- filter_by_minute(medium_test_data2, 30)
bad_test_data_filtered <- filter_by_minute(bad_test_data2, 25)trained_model <- rpart(result ~ ., data = last_training_data, method = "class",
control = rpart.control(cp = 0.001, minsplit = 10, maxdepth = 15))good_predictions <- predict(trained_model, newdata = good_test_data_filtered, type = "class")
medium_predictions <- predict(trained_model, newdata = medium_test_data_filtered, type = "class")
bad_predictions <- predict(trained_model, newdata = bad_test_data_filtered, type = "class")conf_matrix_good_base <- confusionMatrix(good_predictions, good_test_data_filtered$result)
print(conf_matrix_good_base)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 7 5 2
## 1 3 8 1
## 2 3 3 9
##
## Overall Statistics
##
## Accuracy : 0.5854
## 95% CI : (0.4211, 0.7368)
## No Information Rate : 0.3902
## P-Value [Acc > NIR] : 0.0089
##
## Kappa : 0.3815
##
## Mcnemar's Test P-Value : 0.6369
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.5385 0.5000 0.7500
## Specificity 0.7500 0.8400 0.7931
## Pos Pred Value 0.5000 0.6667 0.6000
## Neg Pred Value 0.7778 0.7241 0.8846
## Prevalence 0.3171 0.3902 0.2927
## Detection Rate 0.1707 0.1951 0.2195
## Detection Prevalence 0.3415 0.2927 0.3659
## Balanced Accuracy 0.6442 0.6700 0.7716conf_matrix_medium_base <- confusionMatrix(medium_predictions, medium_test_data_filtered$result)
print(conf_matrix_medium_base)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 1 3 4
## 1 4 6 3
## 2 2 5 5
##
## Overall Statistics
##
## Accuracy : 0.3636
## 95% CI : (0.204, 0.5488)
## No Information Rate : 0.4242
## P-Value [Acc > NIR] : 0.8100
##
## Kappa : 0.0198
##
## Mcnemar's Test P-Value : 0.7269
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.1429 0.4286 0.4167
## Specificity 0.7308 0.6316 0.6667
## Pos Pred Value 0.1250 0.4615 0.4167
## Neg Pred Value 0.7600 0.6000 0.6667
## Prevalence 0.2121 0.4242 0.3636
## Detection Rate 0.0303 0.1818 0.1515
## Detection Prevalence 0.2424 0.3939 0.3636
## Balanced Accuracy 0.4368 0.5301 0.5417conf_matrix_bad_base <- confusionMatrix(bad_predictions, bad_test_data_filtered$result)
print(conf_matrix_bad_base)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 0 4 1
## 1 3 19 3
## 2 1 0 2
##
## Overall Statistics
##
## Accuracy : 0.6364
## 95% CI : (0.4512, 0.796)
## No Information Rate : 0.697
## P-Value [Acc > NIR] : 0.8290
##
## Kappa : 0.1681
##
## Mcnemar's Test P-Value : 0.3701
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.0000 0.8261 0.33333
## Specificity 0.8276 0.4000 0.96296
## Pos Pred Value 0.0000 0.7600 0.66667
## Neg Pred Value 0.8571 0.5000 0.86667
## Prevalence 0.1212 0.6970 0.18182
## Detection Rate 0.0000 0.5758 0.06061
## Detection Prevalence 0.1515 0.7576 0.09091
## Balanced Accuracy 0.4138 0.6130 0.64815good_base_results <- good_test_data_filtered %>%
mutate(
predicted_result = good_predictions,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)pred_probs_good_dt <- predict(trained_model, newdata = good_test_data_filtered, type = "prob")# Define a range of thresholds to test for the Good category
good_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Good category
good_results <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Good category
for (good_thresh in good_thresholds) {
good_results_filtered <- good_test_data_filtered %>%
mutate(
predicted_result_good = good_predictions,
predicted_prob_good = case_when(
predicted_result_good == 1 ~ pred_probs_good_dt[, "1"],
predicted_result_good == 2 ~ pred_probs_good_dt[, "2"],
predicted_result_good == 0 ~ pred_probs_good_dt[, "0"],
TRUE ~ NA_real_
),
match_return_good = case_when(
predicted_prob_good < good_thresh ~ 0,
predicted_result_good == 1 & result == 1 ~ X1,
predicted_result_good == 2 & result == 2 ~ X2,
predicted_result_good == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_good = case_when(
predicted_prob_good < good_thresh ~ 0,
match_return_good > 0 ~ match_return_good,
TRUE ~ -1
)
)
# Calculate total return and profit for the Good category
total_return_good <- sum(good_results_filtered$match_return_good, na.rm = TRUE)
total_profit_good <- sum(good_results_filtered$profit_good, na.rm = TRUE)
# Store results for this threshold
good_results <- rbind(good_results, data.frame(threshold = good_thresh, total_return = total_return_good, total_profit = total_profit_good))
}
# Find the threshold with the highest total profit for the Good category
optimal_good_threshold <- good_results[which.max(good_results$total_profit), ]
# Print the results
print(good_results)## threshold total_return total_profit
## 1 0.50 61.80 44.80
## 2 0.51 61.80 44.80
## 3 0.52 61.80 44.80
## 4 0.53 61.80 44.80
## 5 0.54 54.60 38.60
## 6 0.55 48.48 32.48
## 7 0.56 48.48 32.48
## 8 0.57 48.48 32.48
## 9 0.58 48.48 32.48
## 10 0.59 48.48 32.48
## 11 0.60 48.48 32.48
## 12 0.61 44.88 28.88
## 13 0.62 44.88 28.88
## 14 0.63 44.88 28.88
## 15 0.64 44.88 28.88
## 16 0.65 44.88 28.88
## 17 0.66 42.13 27.13
## 18 0.67 42.13 27.13
## 19 0.68 42.13 28.13
## 20 0.69 42.13 28.13
## 21 0.70 38.73 25.73
## 22 0.71 35.86 24.86
## 23 0.72 35.86 24.86
## 24 0.73 35.86 24.86
## 25 0.74 33.13 26.13
## 26 0.75 33.13 26.13
## 27 0.76 33.13 27.13
## 28 0.77 33.13 27.13
## 29 0.78 27.81 22.81
## 30 0.79 23.31 18.31
## 31 0.80 23.31 19.31
## 32 0.81 23.31 19.31
## 33 0.82 23.31 19.31
## 34 0.83 20.11 16.11
## 35 0.84 17.11 14.11
## 36 0.85 17.11 14.11
## 37 0.86 17.11 16.11
## 38 0.87 17.11 16.11
## 39 0.88 15.61 14.61
## 40 0.89 15.61 14.61
## 41 0.90 15.61 14.61print(paste("Optimal Threshold for Good Category:", optimal_good_threshold$threshold))## [1] "Optimal Threshold for Good Category: 0.5"print(paste("Maximum Total Return for Good Category:", optimal_good_threshold$total_return))## [1] "Maximum Total Return for Good Category: 61.8"print(paste("Maximum Total Profit for Good Category:", optimal_good_threshold$total_profit))## [1] "Maximum Total Profit for Good Category: 44.8"total_return_base_good <- sum(good_base_results$match_return, na.rm = TRUE)
average_return_base_good <- mean(good_base_results$match_return, na.rm = TRUE)
total_profit_base_good <- sum(good_base_results$profit, na.rm = TRUE)
average_profit_base_good <- mean(good_base_results$profit, na.rm = TRUE)
print(paste("Total Return for Good Category:", total_return_base_good))## [1] "Total Return for Good Category: 61.8"print(paste("Average Return per Good Category Match:", average_return_base_good))## [1] "Average Return per Good Category Match: 1.50731707317073"print(paste("Total Profit for Good Category:", total_profit_base_good))## [1] "Total Profit for Good Category: 44.8"print(paste("Average Profit per Good Category Match:", average_profit_base_good))## [1] "Average Profit per Good Category Match: 1.09268292682927"medium_base_results <- medium_test_data_filtered %>%
mutate(
predicted_result = medium_predictions,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)pred_probs_medium_dt <- predict(trained_model, newdata = medium_test_data_filtered, type = "prob")total_return_base_medium <- sum(medium_base_results$match_return, na.rm = TRUE)
average_return_base_medium <- mean(medium_base_results$match_return, na.rm = TRUE)
total_profit_base_medium <- sum(medium_base_results$profit, na.rm = TRUE)
average_profit_base_medium <- mean(medium_base_results$profit, na.rm = TRUE)
print(paste("Total Return for Medium Category:", total_return_base_medium))## [1] "Total Return for Medium Category: 23.04"print(paste("Average Return per Medium Category Match:", average_return_base_medium))## [1] "Average Return per Medium Category Match: 0.698181818181818"print(paste("Total Profit for Medium Category:", total_profit_base_medium))## [1] "Total Profit for Medium Category: 2.04"print(paste("Average Profit per Medium Category Match:", average_profit_base_medium))## [1] "Average Profit per Medium Category Match: 0.0618181818181819"thresholds <- seq(0.50, 0.90, by = 0.01)
results <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
for (thresh in thresholds) {
medium_results <- medium_test_data_filtered %>%
mutate(
predicted_result = medium_predictions,
predicted_prob = case_when(
predicted_result == 1 ~ pred_probs_medium_dt[, "1"],
predicted_result == 2 ~ pred_probs_medium_dt[, "2"],
predicted_result == 0 ~ pred_probs_medium_dt[, "0"],
TRUE ~ NA_real_
),
match_return = case_when(
predicted_prob < thresh ~ 0,
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
predicted_prob < thresh ~ 0,
match_return > 0 ~ match_return,
TRUE ~ -1
)
)
total_return <- sum(medium_results$match_return, na.rm = TRUE)
total_profit <- sum(medium_results$profit, na.rm = TRUE)
results <- rbind(results, data.frame(threshold = thresh, total_return = total_return, total_profit = total_profit))
}
optimal_threshold <- results[which.max(results$total_profit), ]
print(results)## threshold total_return total_profit
## 1 0.50 23.04 2.04
## 2 0.51 23.04 2.04
## 3 0.52 23.04 2.04
## 4 0.53 23.04 2.04
## 5 0.54 23.04 2.04
## 6 0.55 20.67 -0.33
## 7 0.56 20.67 -0.33
## 8 0.57 20.67 -0.33
## 9 0.58 20.67 -0.33
## 10 0.59 20.67 -0.33
## 11 0.60 20.67 1.67
## 12 0.61 17.92 0.92
## 13 0.62 17.92 0.92
## 14 0.63 17.92 2.92
## 15 0.64 13.87 -0.13
## 16 0.65 11.50 -1.50
## 17 0.66 11.50 -1.50
## 18 0.67 11.50 -1.50
## 19 0.68 9.55 -0.45
## 20 0.69 9.55 -0.45
## 21 0.70 9.55 -0.45
## 22 0.71 7.50 -0.50
## 23 0.72 4.74 -3.26
## 24 0.73 4.74 -3.26
## 25 0.74 3.38 -3.62
## 26 0.75 3.38 -3.62
## 27 0.76 3.38 -0.62
## 28 0.77 3.38 -0.62
## 29 0.78 3.38 -0.62
## 30 0.79 3.38 -0.62
## 31 0.80 3.38 0.38
## 32 0.81 1.28 0.28
## 33 0.82 1.28 0.28
## 34 0.83 1.28 0.28
## 35 0.84 1.28 0.28
## 36 0.85 1.28 0.28
## 37 0.86 1.28 0.28
## 38 0.87 1.28 0.28
## 39 0.88 0.00 0.00
## 40 0.89 0.00 0.00
## 41 0.90 0.00 0.00print(paste("Optimal Threshold:", optimal_threshold$threshold))## [1] "Optimal Threshold: 0.63"print(paste("Maximum Total Return:", optimal_threshold$total_return))## [1] "Maximum Total Return: 17.92"print(paste("Maximum Total Profit:", optimal_threshold$total_profit))## [1] "Maximum Total Profit: 2.92"pred_probs_bad_dt <- predict(trained_model, newdata = bad_test_data_filtered, type = "prob")bad_base_results <- bad_test_data_filtered %>%
mutate(
predicted_result = bad_predictions,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)bad_thresholds <- seq(0.50, 0.90, by = 0.01)
bad_results <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
for (bad_thresh in bad_thresholds) {
bad_results_filtered <- bad_test_data_filtered %>%
mutate(
predicted_result_bad = bad_predictions,
predicted_prob_bad = case_when(
predicted_result_bad == 1 ~ pred_probs_bad_dt[, "1"],
predicted_result_bad == 2 ~ pred_probs_bad_dt[, "2"],
predicted_result_bad == 0 ~ pred_probs_bad_dt[, "0"],
TRUE ~ NA_real_
),
match_return_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0,
predicted_result_bad == 1 & result == 1 ~ X1,
predicted_result_bad == 2 & result == 2 ~ X2,
predicted_result_bad == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0,
match_return_bad > 0 ~ match_return_bad,
TRUE ~ -1
)
)
# Calculate total return and profit for the Bad category
total_return_bad <- sum(bad_results_filtered$match_return_bad, na.rm = TRUE)
total_profit_bad <- sum(bad_results_filtered$profit_bad, na.rm = TRUE)
# Store results for this threshold
bad_results <- rbind(bad_results, data.frame(threshold = bad_thresh, total_return = total_return_bad, total_profit = total_profit_bad))
}
# Find the threshold with the highest total profit for the Bad category
optimal_bad_threshold <- bad_results[which.max(bad_results$total_profit), ]
# Print the results
print(bad_results)## threshold total_return total_profit
## 1 0.50 26.50 14.50
## 2 0.51 26.50 14.50
## 3 0.52 26.50 14.50
## 4 0.53 26.50 14.50
## 5 0.54 26.50 14.50
## 6 0.55 26.50 14.50
## 7 0.56 26.50 14.50
## 8 0.57 26.50 14.50
## 9 0.58 26.50 14.50
## 10 0.59 26.50 14.50
## 11 0.60 26.50 14.50
## 12 0.61 26.50 14.50
## 13 0.62 26.50 14.50
## 14 0.63 26.50 14.50
## 15 0.64 26.50 14.50
## 16 0.65 26.50 15.50
## 17 0.66 26.50 15.50
## 18 0.67 26.50 15.50
## 19 0.68 24.89 15.89
## 20 0.69 22.79 13.79
## 21 0.70 21.18 14.18
## 22 0.71 21.18 14.18
## 23 0.72 17.34 11.34
## 24 0.73 17.34 11.34
## 25 0.74 17.34 11.34
## 26 0.75 17.34 11.34
## 27 0.76 17.34 12.34
## 28 0.77 17.34 12.34
## 29 0.78 17.34 12.34
## 30 0.79 17.34 12.34
## 31 0.80 17.34 12.34
## 32 0.81 17.34 12.34
## 33 0.82 17.34 12.34
## 34 0.83 17.34 13.34
## 35 0.84 17.34 13.34
## 36 0.85 17.34 13.34
## 37 0.86 17.34 13.34
## 38 0.87 17.34 13.34
## 39 0.88 8.55 6.55
## 40 0.89 8.55 7.55
## 41 0.90 8.55 7.55print(paste("Optimal Threshold for Bad Category:", optimal_bad_threshold$threshold))## [1] "Optimal Threshold for Bad Category: 0.68"print(paste("Maximum Total Return for Bad Category:", optimal_bad_threshold$total_return))## [1] "Maximum Total Return for Bad Category: 24.89"print(paste("Maximum Total Profit for Bad Category:", optimal_bad_threshold$total_profit))## [1] "Maximum Total Profit for Bad Category: 15.89"total_return_base_bad <- sum(bad_base_results$match_return, na.rm = TRUE)
average_return_base_bad <- mean(bad_base_results$match_return, na.rm = TRUE)
total_profit_base_bad <- sum(bad_base_results$profit, na.rm = TRUE)
average_profit_base_bad <- mean(bad_base_results$profit, na.rm = TRUE)
print(paste("Total Return for Bad Category:", total_return_base_bad))## [1] "Total Return for Bad Category: 26.5"print(paste("Average Return per Bad Category Match:", average_return_base_bad))## [1] "Average Return per Bad Category Match: 0.803030303030303"print(paste("Total Profit for Bad Category:", total_profit_base_bad))## [1] "Total Profit for Bad Category: 14.5"print(paste("Average Profit per Bad Category Match:", average_profit_base_bad))## [1] "Average Profit per Bad Category Match: 0.439393939393939"pred_probs_good_dt <- predict(trained_model, newdata = good_test_data_filtered, type = "prob")good_predictions_multinom <- predict(multinom_model, newdata = good_test_data_filtered, type = "class")
medium_predictions_multinom <- predict(multinom_model, newdata = medium_test_data_filtered, type = "class")
bad_predictions_multinom <- predict(multinom_model, newdata = bad_test_data_filtered, type = "class")conf_matrix_good_multinom <- confusionMatrix(good_predictions_multinom, good_test_data_filtered$result)
print(conf_matrix_good_multinom)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 1 7 5
## 1 6 6 1
## 2 6 3 6
##
## Overall Statistics
##
## Accuracy : 0.3171
## 95% CI : (0.1808, 0.4809)
## No Information Rate : 0.3902
## P-Value [Acc > NIR] : 0.8696
##
## Kappa : -0.0214
##
## Mcnemar's Test P-Value : 0.7607
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.07692 0.3750 0.5000
## Specificity 0.57143 0.7200 0.6897
## Pos Pred Value 0.07692 0.4615 0.4000
## Neg Pred Value 0.57143 0.6429 0.7692
## Prevalence 0.31707 0.3902 0.2927
## Detection Rate 0.02439 0.1463 0.1463
## Detection Prevalence 0.31707 0.3171 0.3659
## Balanced Accuracy 0.32418 0.5475 0.5948conf_matrix_medium_multinom <- confusionMatrix(medium_predictions_multinom, medium_test_data_filtered$result)
print(conf_matrix_medium_multinom)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 6 5 3
## 1 0 6 2
## 2 1 3 7
##
## Overall Statistics
##
## Accuracy : 0.5758
## 95% CI : (0.3922, 0.7452)
## No Information Rate : 0.4242
## P-Value [Acc > NIR] : 0.05732
##
## Kappa : 0.3815
##
## Mcnemar's Test P-Value : 0.10228
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.8571 0.4286 0.5833
## Specificity 0.6923 0.8947 0.8095
## Pos Pred Value 0.4286 0.7500 0.6364
## Neg Pred Value 0.9474 0.6800 0.7727
## Prevalence 0.2121 0.4242 0.3636
## Detection Rate 0.1818 0.1818 0.2121
## Detection Prevalence 0.4242 0.2424 0.3333
## Balanced Accuracy 0.7747 0.6617 0.6964conf_matrix_bad_multinom <- confusionMatrix(bad_predictions_multinom, bad_test_data_filtered$result)
print(conf_matrix_bad_multinom)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 0 2 0
## 1 3 21 3
## 2 1 0 3
##
## Overall Statistics
##
## Accuracy : 0.7273
## 95% CI : (0.5448, 0.867)
## No Information Rate : 0.697
## P-Value [Acc > NIR] : 0.4347
##
## Kappa : 0.3188
##
## Mcnemar's Test P-Value : 0.2407
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.00000 0.9130 0.50000
## Specificity 0.93103 0.4000 0.96296
## Pos Pred Value 0.00000 0.7778 0.75000
## Neg Pred Value 0.87097 0.6667 0.89655
## Prevalence 0.12121 0.6970 0.18182
## Detection Rate 0.00000 0.6364 0.09091
## Detection Prevalence 0.06061 0.8182 0.12121
## Balanced Accuracy 0.46552 0.6565 0.73148pred_probs_good_multinom <- predict(multinom_model, newdata = good_test_data_filtered, type = "prob")
pred_probs_medium_multinom <- predict(multinom_model, newdata = medium_test_data_filtered, type = "prob")
pred_probs_bad_multinom <- predict(multinom_model, newdata = bad_test_data_filtered, type = "prob")good_multinom_results <- good_test_data_filtered %>%
mutate(
predicted_result = good_predictions_multinom,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Good category
good_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Good category
good_results_multinom <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Good category
for (good_thresh in good_thresholds) {
good_results_filtered <- good_test_data_filtered %>%
mutate(
predicted_result_good = good_predictions_multinom, # Predictions from multinom model
predicted_prob_good = case_when(
predicted_result_good == 1 ~ pred_probs_good_multinom[, "1"],
predicted_result_good == 2 ~ pred_probs_good_multinom[, "2"],
predicted_result_good == 0 ~ pred_probs_good_multinom[, "0"],
TRUE ~ NA_real_
),
match_return_good = case_when(
predicted_prob_good < good_thresh ~ 0, # No bet if below threshold
predicted_result_good == 1 & result == 1 ~ X1,
predicted_result_good == 2 & result == 2 ~ X2,
predicted_result_good == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_good = case_when(
predicted_prob_good < good_thresh ~ 0, # No bet if below threshold
match_return_good > 0 ~ match_return_good,
TRUE ~ -1
)
)
# Calculate total return and profit for the Good category
total_return_good <- sum(good_results_filtered$match_return_good, na.rm = TRUE)
total_profit_good <- sum(good_results_filtered$profit_good, na.rm = TRUE)
# Store results for this threshold
good_results_multinom <- rbind(
good_results_multinom,
data.frame(threshold = good_thresh, total_return = total_return_good, total_profit = total_profit_good)
)
}
# Find the threshold with the highest total profit for the Good category
optimal_good_threshold_multinom <- good_results_multinom[which.max(good_results_multinom$total_profit), ]
# Print the results
print(good_results_multinom)## threshold total_return total_profit
## 1 0.50 13.32 4.32
## 2 0.51 13.32 4.32
## 3 0.52 13.32 5.32
## 4 0.53 10.57 3.57
## 5 0.54 10.57 4.57
## 6 0.55 10.57 5.57
## 7 0.56 9.37 5.37
## 8 0.57 9.37 5.37
## 9 0.58 9.37 5.37
## 10 0.59 9.37 5.37
## 11 0.60 6.15 2.15
## 12 0.61 6.15 3.15
## 13 0.62 4.75 2.75
## 14 0.63 4.75 2.75
## 15 0.64 4.75 2.75
## 16 0.65 4.75 3.75
## 17 0.66 4.75 3.75
## 18 0.67 4.75 3.75
## 19 0.68 3.59 2.59
## 20 0.69 3.59 3.59
## 21 0.70 2.43 2.43
## 22 0.71 2.43 2.43
## 23 0.72 2.43 2.43
## 24 0.73 2.43 2.43
## 25 0.74 2.43 2.43
## 26 0.75 2.43 2.43
## 27 0.76 1.10 1.10
## 28 0.77 1.10 1.10
## 29 0.78 1.10 1.10
## 30 0.79 1.10 1.10
## 31 0.80 1.10 1.10
## 32 0.81 1.10 1.10
## 33 0.82 1.10 1.10
## 34 0.83 1.10 1.10
## 35 0.84 0.00 0.00
## 36 0.85 0.00 0.00
## 37 0.86 0.00 0.00
## 38 0.87 0.00 0.00
## 39 0.88 0.00 0.00
## 40 0.89 0.00 0.00
## 41 0.90 0.00 0.00print(paste("Optimal Threshold for Good Category:", optimal_good_threshold_multinom$threshold))## [1] "Optimal Threshold for Good Category: 0.55"print(paste("Maximum Total Return for Good Category:", optimal_good_threshold_multinom$total_return))## [1] "Maximum Total Return for Good Category: 10.57"print(paste("Maximum Total Profit for Good Category:", optimal_good_threshold_multinom$total_profit))## [1] "Maximum Total Profit for Good Category: 5.57"total_return_multinom_good <- sum(good_multinom_results$match_return, na.rm = TRUE)
average_return_multinom_good <- mean(good_multinom_results$match_return, na.rm = TRUE)
total_profit_multinom_good <- sum(good_multinom_results$profit, na.rm = TRUE)
average_profit_multinom_good <- mean(good_multinom_results$profit, na.rm = TRUE)
print(paste("Total Return for Good Category:", total_return_multinom_good))## [1] "Total Return for Good Category: 20.63"print(paste("Average Return per Good Category Match:", average_return_multinom_good))## [1] "Average Return per Good Category Match: 0.503170731707317"print(paste("Total Profit for Good Category:", total_profit_multinom_good))## [1] "Total Profit for Good Category: -7.37"print(paste("Average Profit per Good Category Match:", average_profit_multinom_good))## [1] "Average Profit per Good Category Match: -0.179756097560976"medium_multinom_results <- medium_test_data_filtered %>%
mutate(
predicted_result = medium_predictions_multinom,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Medium category
medium_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Medium category
medium_results_multinom <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Medium category
for (medium_thresh in medium_thresholds) {
medium_results_filtered <- medium_test_data_filtered %>%
mutate(
predicted_result_medium = medium_predictions_multinom,
predicted_prob_medium = case_when(
predicted_result_medium == 1 ~ pred_probs_medium_multinom[, "1"],
predicted_result_medium == 2 ~ pred_probs_medium_multinom[, "2"],
predicted_result_medium == 0 ~ pred_probs_medium_multinom[, "0"],
TRUE ~ NA_real_
),
match_return_medium = case_when(
predicted_prob_medium < medium_thresh ~ 0,
predicted_result_medium == 1 & result == 1 ~ X1,
predicted_result_medium == 2 & result == 2 ~ X2,
predicted_result_medium == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_medium = case_when(
predicted_prob_medium < medium_thresh ~ 0,
match_return_medium > 0 ~ match_return_medium,
TRUE ~ -1
)
)
# Calculate total return and profit for the Medium category
total_return_medium <- sum(medium_results_filtered$match_return_medium, na.rm = TRUE)
total_profit_medium <- sum(medium_results_filtered$profit_medium, na.rm = TRUE)
# Store results for this threshold
medium_results_multinom <- rbind(
medium_results_multinom,
data.frame(threshold = medium_thresh, total_return = total_return_medium, total_profit = total_profit_medium)
)
}
# Find the threshold with the highest total profit for the Medium category
optimal_medium_threshold_multinom <- medium_results_multinom[which.max(medium_results_multinom$total_profit), ]
# Print the results
print(medium_results_multinom)## threshold total_return total_profit
## 1 0.50 14.98 6.98
## 2 0.51 13.03 5.03
## 3 0.52 13.03 5.03
## 4 0.53 13.03 6.03
## 5 0.54 13.03 6.03
## 6 0.55 13.03 7.03
## 7 0.56 13.03 7.03
## 8 0.57 13.03 7.03
## 9 0.58 13.03 8.03
## 10 0.59 13.03 8.03
## 11 0.60 8.63 4.63
## 12 0.61 8.63 4.63
## 13 0.62 8.63 4.63
## 14 0.63 8.63 5.63
## 15 0.64 8.63 7.63
## 16 0.65 8.63 7.63
## 17 0.66 7.27 6.27
## 18 0.67 4.02 3.02
## 19 0.68 4.02 3.02
## 20 0.69 4.02 3.02
## 21 0.70 4.02 3.02
## 22 0.71 4.02 3.02
## 23 0.72 1.36 0.36
## 24 0.73 1.36 0.36
## 25 0.74 1.36 0.36
## 26 0.75 1.36 0.36
## 27 0.76 1.36 0.36
## 28 0.77 1.36 0.36
## 29 0.78 1.36 1.36
## 30 0.79 1.36 1.36
## 31 0.80 1.36 1.36
## 32 0.81 1.36 1.36
## 33 0.82 1.36 1.36
## 34 0.83 1.36 1.36
## 35 0.84 1.36 1.36
## 36 0.85 0.00 0.00
## 37 0.86 0.00 0.00
## 38 0.87 0.00 0.00
## 39 0.88 0.00 0.00
## 40 0.89 0.00 0.00
## 41 0.90 0.00 0.00print(paste("Optimal Threshold for Medium Category:", optimal_medium_threshold_multinom$threshold))## [1] "Optimal Threshold for Medium Category: 0.58"print(paste("Maximum Total Return for Medium Category:", optimal_medium_threshold_multinom$total_return))## [1] "Maximum Total Return for Medium Category: 13.03"print(paste("Maximum Total Profit for Medium Category:", optimal_medium_threshold_multinom$total_profit))## [1] "Maximum Total Profit for Medium Category: 8.03"# Calculate total and average return and profit for the Medium category
total_return_multinom_medium <- sum(medium_multinom_results$match_return, na.rm = TRUE)
average_return_multinom_medium <- mean(medium_multinom_results$match_return, na.rm = TRUE)
total_profit_multinom_medium <- sum(medium_multinom_results$profit, na.rm = TRUE)
average_profit_multinom_medium <- mean(medium_multinom_results$profit, na.rm = TRUE)
# Print results for the Medium category
print(paste("Total Return for Medium Category:", total_return_multinom_medium))## [1] "Total Return for Medium Category: 40.38"print(paste("Average Return per Medium Category Match:", average_return_multinom_medium))## [1] "Average Return per Medium Category Match: 1.22363636363636"print(paste("Total Profit for Medium Category:", total_profit_multinom_medium))## [1] "Total Profit for Medium Category: 26.38"print(paste("Average Profit per Medium Category Match:", average_profit_multinom_medium))## [1] "Average Profit per Medium Category Match: 0.799393939393939"bad_multinom_results <- bad_test_data_filtered %>%
mutate(
predicted_result = bad_predictions_multinom,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Bad category
bad_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Bad category
bad_results_multinom <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Bad category
for (bad_thresh in bad_thresholds) {
bad_results_filtered <- bad_test_data_filtered %>%
mutate(
predicted_result_bad = bad_predictions_multinom, # Predictions from multinom model
predicted_prob_bad = case_when(
predicted_result_bad == 1 ~ pred_probs_bad_multinom[, "1"],
predicted_result_bad == 2 ~ pred_probs_bad_multinom[, "2"],
predicted_result_bad == 0 ~ pred_probs_bad_multinom[, "0"],
TRUE ~ NA_real_
),
match_return_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0, # No bet if below threshold
predicted_result_bad == 1 & result == 1 ~ X1,
predicted_result_bad == 2 & result == 2 ~ X2,
predicted_result_bad == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0, # No bet if below threshold
match_return_bad > 0 ~ match_return_bad,
TRUE ~ -1
)
)
# Calculate total return and profit for the Bad category
total_return_bad <- sum(bad_results_filtered$match_return_bad, na.rm = TRUE)
total_profit_bad <- sum(bad_results_filtered$profit_bad, na.rm = TRUE)
# Store results for this threshold
bad_results_multinom <- rbind(
bad_results_multinom,
data.frame(threshold = bad_thresh, total_return = total_return_bad, total_profit = total_profit_bad)
)
}
# Find the threshold with the highest total profit for the Bad category
optimal_bad_threshold_multinom <- bad_results_multinom[which.max(bad_results_multinom$total_profit), ]
# Print the results
print(bad_results_multinom)## threshold total_return total_profit
## 1 0.50 31.35 25.35
## 2 0.51 30.17 24.17
## 3 0.52 30.17 24.17
## 4 0.53 28.51 22.51
## 5 0.54 28.51 22.51
## 6 0.55 28.51 22.51
## 7 0.56 27.11 21.11
## 8 0.57 27.11 22.11
## 9 0.58 25.45 20.45
## 10 0.59 23.84 18.84
## 11 0.60 22.64 17.64
## 12 0.61 21.03 16.03
## 13 0.62 17.71 13.71
## 14 0.63 16.31 13.31
## 15 0.64 16.31 13.31
## 16 0.65 16.31 13.31
## 17 0.66 14.98 12.98
## 18 0.67 13.37 11.37
## 19 0.68 12.15 11.15
## 20 0.69 12.15 11.15
## 21 0.70 12.15 11.15
## 22 0.71 12.15 11.15
## 23 0.72 12.15 11.15
## 24 0.73 11.14 10.14
## 25 0.74 6.65 5.65
## 26 0.75 6.65 5.65
## 27 0.76 5.55 4.55
## 28 0.77 4.33 3.33
## 29 0.78 3.28 3.28
## 30 0.79 3.28 3.28
## 31 0.80 3.28 3.28
## 32 0.81 3.28 3.28
## 33 0.82 3.28 3.28
## 34 0.83 1.22 1.22
## 35 0.84 0.00 0.00
## 36 0.85 0.00 0.00
## 37 0.86 0.00 0.00
## 38 0.87 0.00 0.00
## 39 0.88 0.00 0.00
## 40 0.89 0.00 0.00
## 41 0.90 0.00 0.00print(paste("Optimal Threshold for Bad Category:", optimal_bad_threshold_multinom$threshold))## [1] "Optimal Threshold for Bad Category: 0.5"print(paste("Maximum Total Return for Bad Category:", optimal_bad_threshold_multinom$total_return))## [1] "Maximum Total Return for Bad Category: 31.35"print(paste("Maximum Total Profit for Bad Category:", optimal_bad_threshold_multinom$total_profit))## [1] "Maximum Total Profit for Bad Category: 25.35"total_return_multinom_bad <- sum(bad_multinom_results$match_return, na.rm = TRUE)
average_return_multinom_bad <- mean(bad_multinom_results$match_return, na.rm = TRUE)
total_profit_multinom_bad <- sum(bad_multinom_results$profit, na.rm = TRUE)
average_profit_multinom_bad <- mean(bad_multinom_results$profit, na.rm = TRUE)
print(paste("Total Return for Bad Category:", total_return_multinom_bad))## [1] "Total Return for Bad Category: 31.35"print(paste("Average Return per Bad Category Match:", average_return_multinom_bad))## [1] "Average Return per Bad Category Match: 0.95"print(paste("Total Profit for Bad Category:", total_profit_multinom_bad))## [1] "Total Profit for Bad Category: 22.35"print(paste("Average Profit per Bad Category Match:", average_profit_multinom_bad))## [1] "Average Profit per Bad Category Match: 0.677272727272727"library(randomForest)
rf_model <- randomForest(result ~ ., data = last_training_data,
mtry = 3,
ntree = 300,
maxnodes = 10,
importance = TRUE
)good_predictions_rf <- predict(rf_model, newdata = good_test_data_filtered, type = "response")
medium_predictions_rf <- predict(rf_model, newdata = medium_test_data_filtered, type = "response")
bad_predictions_rf <- predict(rf_model, newdata = bad_test_data_filtered, type = "response")pred_probs_good_rf <- predict(rf_model, newdata = good_test_data_filtered, type = "prob")
pred_probs_medium_rf <- predict(rf_model, newdata = medium_test_data_filtered, type = "prob")
pred_probs_bad_rf <- predict(rf_model, newdata = bad_test_data_filtered, type = "prob")conf_matrix_good_rf <- confusionMatrix(good_predictions_rf, good_test_data_filtered$result)
print(conf_matrix_good_rf)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 0 0 0
## 1 6 13 4
## 2 7 3 8
##
## Overall Statistics
##
## Accuracy : 0.5122
## 95% CI : (0.3513, 0.6712)
## No Information Rate : 0.3902
## P-Value [Acc > NIR] : 0.076116
##
## Kappa : 0.2525
##
## Mcnemar's Test P-Value : 0.004338
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.0000 0.8125 0.6667
## Specificity 1.0000 0.6000 0.6552
## Pos Pred Value NaN 0.5652 0.4444
## Neg Pred Value 0.6829 0.8333 0.8261
## Prevalence 0.3171 0.3902 0.2927
## Detection Rate 0.0000 0.3171 0.1951
## Detection Prevalence 0.0000 0.5610 0.4390
## Balanced Accuracy 0.5000 0.7063 0.6609conf_matrix_medium_rf <- confusionMatrix(medium_predictions_rf, medium_test_data_filtered$result)
print(conf_matrix_medium_rf)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 0 0 0
## 1 5 11 3
## 2 2 3 9
##
## Overall Statistics
##
## Accuracy : 0.6061
## 95% CI : (0.4214, 0.7709)
## No Information Rate : 0.4242
## P-Value [Acc > NIR] : 0.02703
##
## Kappa : 0.345
##
## Mcnemar's Test P-Value : 0.07190
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.0000 0.7857 0.7500
## Specificity 1.0000 0.5789 0.7619
## Pos Pred Value NaN 0.5789 0.6429
## Neg Pred Value 0.7879 0.7857 0.8421
## Prevalence 0.2121 0.4242 0.3636
## Detection Rate 0.0000 0.3333 0.2727
## Detection Prevalence 0.0000 0.5758 0.4242
## Balanced Accuracy 0.5000 0.6823 0.7560conf_matrix_bad_rf <- confusionMatrix(bad_predictions_rf, bad_test_data_filtered$result)
print(conf_matrix_bad_rf)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 0 0 0
## 1 3 23 3
## 2 1 0 3
##
## Overall Statistics
##
## Accuracy : 0.7879
## 95% CI : (0.6109, 0.9102)
## No Information Rate : 0.697
## P-Value [Acc > NIR] : 0.1725
##
## Kappa : 0.4196
##
## Mcnemar's Test P-Value : 0.0719
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.0000 1.0000 0.50000
## Specificity 1.0000 0.4000 0.96296
## Pos Pred Value NaN 0.7931 0.75000
## Neg Pred Value 0.8788 1.0000 0.89655
## Prevalence 0.1212 0.6970 0.18182
## Detection Rate 0.0000 0.6970 0.09091
## Detection Prevalence 0.0000 0.8788 0.12121
## Balanced Accuracy 0.5000 0.7000 0.73148good_rf_results <- good_test_data_filtered %>%
mutate(
predicted_result = good_predictions_rf,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Good category
good_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Good category
good_results_rf <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Good category
for (good_thresh in good_thresholds) {
good_results_filtered <- good_test_data_filtered %>%
mutate(
predicted_result_good = good_predictions_rf, # Predictions from Random Forest model
predicted_prob_good = case_when(
predicted_result_good == 1 ~ pred_probs_good_rf[, "1"],
predicted_result_good == 2 ~ pred_probs_good_rf[, "2"],
predicted_result_good == 0 ~ pred_probs_good_rf[, "0"],
TRUE ~ NA_real_
),
match_return_good = case_when(
predicted_prob_good < good_thresh ~ 0, # No bet if below threshold
predicted_result_good == 1 & result == 1 ~ X1,
predicted_result_good == 2 & result == 2 ~ X2,
predicted_result_good == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_good = case_when(
predicted_prob_good < good_thresh ~ 0, # No bet if below threshold
match_return_good > 0 ~ match_return_good,
TRUE ~ -1
)
)
# Calculate total return and profit for the Good category
total_return_good <- sum(good_results_filtered$match_return_good, na.rm = TRUE)
total_profit_good <- sum(good_results_filtered$profit_good, na.rm = TRUE)
# Store results for this threshold
good_results_rf <- rbind(
good_results_rf,
data.frame(threshold = good_thresh, total_return = total_return_good, total_profit = total_profit_good)
)
}
# Find the threshold with the highest total profit for the Good category
optimal_good_threshold_rf <- good_results_rf[which.max(good_results_rf$total_profit), ]
# Print the results
print(good_results_rf)## threshold total_return total_profit
## 1 0.50 30.50 17.50
## 2 0.51 27.88 14.88
## 3 0.52 27.88 16.88
## 4 0.53 24.63 14.63
## 5 0.54 24.63 16.63
## 6 0.55 16.66 8.66
## 7 0.56 16.66 8.66
## 8 0.57 16.66 8.66
## 9 0.58 16.66 8.66
## 10 0.59 16.66 8.66
## 11 0.60 16.66 9.66
## 12 0.61 14.56 7.56
## 13 0.62 14.56 7.56
## 14 0.63 14.56 7.56
## 15 0.64 14.56 8.56
## 16 0.65 12.84 6.84
## 17 0.66 12.84 6.84
## 18 0.67 12.84 7.84
## 19 0.68 11.68 6.68
## 20 0.69 11.68 7.68
## 21 0.70 11.68 7.68
## 22 0.71 11.68 7.68
## 23 0.72 10.28 7.28
## 24 0.73 10.28 7.28
## 25 0.74 10.28 7.28
## 26 0.75 9.08 6.08
## 27 0.76 9.08 6.08
## 28 0.77 9.08 6.08
## 29 0.78 9.08 6.08
## 30 0.79 9.08 6.08
## 31 0.80 7.75 4.75
## 32 0.81 7.75 4.75
## 33 0.82 6.65 3.65
## 34 0.83 6.65 4.65
## 35 0.84 6.65 5.65
## 36 0.85 6.65 5.65
## 37 0.86 6.65 5.65
## 38 0.87 6.65 5.65
## 39 0.88 6.65 5.65
## 40 0.89 6.65 5.65
## 41 0.90 5.15 4.15print(paste("Optimal Threshold for Good Category:", optimal_good_threshold_rf$threshold))## [1] "Optimal Threshold for Good Category: 0.5"print(paste("Maximum Total Return for Good Category:", optimal_good_threshold_rf$total_return))## [1] "Maximum Total Return for Good Category: 30.5"print(paste("Maximum Total Profit for Good Category:", optimal_good_threshold_rf$total_profit))## [1] "Maximum Total Profit for Good Category: 17.5"total_return_rf_good <- sum(good_rf_results$match_return, na.rm = TRUE)
average_return_rf_good <- mean(good_rf_results$match_return, na.rm = TRUE)
total_profit_rf_good <- sum(good_rf_results$profit, na.rm = TRUE)
average_profit_rf_good <- mean(good_rf_results$profit, na.rm = TRUE)
print(paste("Total Return for Good Category (RF):", total_return_rf_good))## [1] "Total Return for Good Category (RF): 41.75"print(paste("Average Return per Good Category Match (RF):", average_return_rf_good))## [1] "Average Return per Good Category Match (RF): 1.01829268292683"print(paste("Total Profit for Good Category (RF):", total_profit_rf_good))## [1] "Total Profit for Good Category (RF): 21.75"print(paste("Average Profit per Good Category Match (RF):", average_profit_rf_good))## [1] "Average Profit per Good Category Match (RF): 0.530487804878049"medium_rf_results <- medium_test_data_filtered %>%
mutate(
predicted_result = medium_predictions_rf,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Medium category
medium_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Medium category
medium_results_rf <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Medium category
for (medium_thresh in medium_thresholds) {
medium_results_filtered <- medium_test_data_filtered %>%
mutate(
predicted_result_medium = medium_predictions_rf, # Predictions from Random Forest model
predicted_prob_medium = case_when(
predicted_result_medium == 1 ~ pred_probs_medium_rf[, "1"],
predicted_result_medium == 2 ~ pred_probs_medium_rf[, "2"],
predicted_result_medium == 0 ~ pred_probs_medium_rf[, "0"],
TRUE ~ NA_real_
),
match_return_medium = case_when(
predicted_prob_medium < medium_thresh ~ 0, # No bet if below threshold
predicted_result_medium == 1 & result == 1 ~ X1,
predicted_result_medium == 2 & result == 2 ~ X2,
predicted_result_medium == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_medium = case_when(
predicted_prob_medium < medium_thresh ~ 0, # No bet if below threshold
match_return_medium > 0 ~ match_return_medium,
TRUE ~ -1
)
)
# Calculate total return and profit for the Medium category
total_return_medium <- sum(medium_results_filtered$match_return_medium, na.rm = TRUE)
total_profit_medium <- sum(medium_results_filtered$profit_medium, na.rm = TRUE)
# Store results for this threshold
medium_results_rf <- rbind(
medium_results_rf,
data.frame(threshold = medium_thresh, total_return = total_return_medium, total_profit = total_profit_medium)
)
}
# Find the threshold with the highest total profit for the Medium category
optimal_medium_threshold_rf <- medium_results_rf[which.max(medium_results_rf$total_profit), ]
# Print the results
print(medium_results_rf)## threshold total_return total_profit
## 1 0.50 26.31 16.31
## 2 0.51 26.31 17.31
## 3 0.52 26.31 17.31
## 4 0.53 26.31 17.31
## 5 0.54 24.26 16.26
## 6 0.55 22.16 15.16
## 7 0.56 19.79 12.79
## 8 0.57 19.79 12.79
## 9 0.58 19.79 12.79
## 10 0.59 19.79 12.79
## 11 0.60 17.69 10.69
## 12 0.61 17.69 10.69
## 13 0.62 17.69 10.69
## 14 0.63 17.69 10.69
## 15 0.64 17.69 11.69
## 16 0.65 17.69 11.69
## 17 0.66 15.59 9.59
## 18 0.67 15.59 9.59
## 19 0.68 15.59 9.59
## 20 0.69 11.69 5.69
## 21 0.70 11.69 5.69
## 22 0.71 11.69 5.69
## 23 0.72 11.69 6.69
## 24 0.73 9.00 5.00
## 25 0.74 9.00 5.00
## 26 0.75 9.00 6.00
## 27 0.76 7.67 4.67
## 28 0.77 7.67 4.67
## 29 0.78 7.67 4.67
## 30 0.79 7.67 4.67
## 31 0.80 7.67 4.67
## 32 0.81 7.67 5.67
## 33 0.82 5.84 4.84
## 34 0.83 4.04 3.04
## 35 0.84 4.04 4.04
## 36 0.85 4.04 4.04
## 37 0.86 4.04 4.04
## 38 0.87 4.04 4.04
## 39 0.88 4.04 4.04
## 40 0.89 4.04 4.04
## 41 0.90 4.04 4.04print(paste("Optimal Threshold for Medium Category:", optimal_medium_threshold_rf$threshold))## [1] "Optimal Threshold for Medium Category: 0.51"print(paste("Maximum Total Return for Medium Category:", optimal_medium_threshold_rf$total_return))## [1] "Maximum Total Return for Medium Category: 26.31"print(paste("Maximum Total Profit for Medium Category:", optimal_medium_threshold_rf$total_profit))## [1] "Maximum Total Profit for Medium Category: 17.31"# Calculate total and average return and profit for the Medium category
total_return_rf_medium <- sum(medium_rf_results$match_return, na.rm = TRUE)
average_return_rf_medium <- mean(medium_rf_results$match_return, na.rm = TRUE)
total_profit_rf_medium <- sum(medium_rf_results$profit, na.rm = TRUE)
average_profit_rf_medium <- mean(medium_rf_results$profit, na.rm = TRUE)
# Print results for the Medium category
print(paste("Total Return for Medium Category (RF):", total_return_rf_medium))## [1] "Total Return for Medium Category (RF): 38.08"print(paste("Average Return per Medium Category Match (RF):", average_return_rf_medium))## [1] "Average Return per Medium Category Match (RF): 1.15393939393939"print(paste("Total Profit for Medium Category (RF):", total_profit_rf_medium))## [1] "Total Profit for Medium Category (RF): 25.08"print(paste("Average Profit per Medium Category Match (RF):", average_profit_rf_medium))## [1] "Average Profit per Medium Category Match (RF): 0.76"bad_rf_results <- bad_test_data_filtered %>%
mutate(
predicted_result = bad_predictions_rf,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Bad category
bad_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Bad category
bad_results_rf <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Bad category
for (bad_thresh in bad_thresholds) {
bad_results_filtered <- bad_test_data_filtered %>%
mutate(
predicted_result_bad = bad_predictions_rf, # Predictions from Random Forest model
predicted_prob_bad = case_when(
predicted_result_bad == 1 ~ pred_probs_bad_rf[, "1"],
predicted_result_bad == 2 ~ pred_probs_bad_rf[, "2"],
predicted_result_bad == 0 ~ pred_probs_bad_rf[, "0"],
TRUE ~ NA_real_
),
match_return_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0, # No bet if below threshold
predicted_result_bad == 1 & result == 1 ~ X1,
predicted_result_bad == 2 & result == 2 ~ X2,
predicted_result_bad == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0, # No bet if below threshold
match_return_bad > 0 ~ match_return_bad,
TRUE ~ -1
)
)
# Calculate total return and profit for the Bad category
total_return_bad <- sum(bad_results_filtered$match_return_bad, na.rm = TRUE)
total_profit_bad <- sum(bad_results_filtered$profit_bad, na.rm = TRUE)
# Store results for this threshold
bad_results_rf <- rbind(
bad_results_rf,
data.frame(threshold = bad_thresh, total_return = total_return_bad, total_profit = total_profit_bad)
)
}
# Find the threshold with the highest total profit for the Bad category
optimal_bad_threshold_rf <- bad_results_rf[which.max(bad_results_rf$total_profit), ]
# Print the results
print(bad_results_rf)## threshold total_return total_profit
## 1 0.50 33.42 26.42
## 2 0.51 33.42 26.42
## 3 0.52 31.76 24.76
## 4 0.53 31.76 24.76
## 5 0.54 31.76 24.76
## 6 0.55 31.76 24.76
## 7 0.56 31.76 24.76
## 8 0.57 28.89 21.89
## 9 0.58 28.89 21.89
## 10 0.59 28.89 21.89
## 11 0.60 28.89 21.89
## 12 0.61 28.89 21.89
## 13 0.62 28.89 21.89
## 14 0.63 28.89 21.89
## 15 0.64 28.89 21.89
## 16 0.65 28.89 21.89
## 17 0.66 28.89 21.89
## 18 0.67 28.89 21.89
## 19 0.68 28.89 21.89
## 20 0.69 28.89 21.89
## 21 0.70 28.89 21.89
## 22 0.71 27.84 20.84
## 23 0.72 27.84 20.84
## 24 0.73 27.84 20.84
## 25 0.74 27.84 20.84
## 26 0.75 27.84 21.84
## 27 0.76 27.84 21.84
## 28 0.77 26.23 21.23
## 29 0.78 26.23 21.23
## 30 0.79 26.23 21.23
## 31 0.80 26.23 21.23
## 32 0.81 26.23 21.23
## 33 0.82 26.23 21.23
## 34 0.83 26.23 21.23
## 35 0.84 23.81 19.81
## 36 0.85 23.81 19.81
## 37 0.86 23.81 19.81
## 38 0.87 23.81 19.81
## 39 0.88 18.93 16.93
## 40 0.89 18.93 18.93
## 41 0.90 18.93 18.93print(paste("Optimal Threshold for Bad Category:", optimal_bad_threshold_rf$threshold))## [1] "Optimal Threshold for Bad Category: 0.5"print(paste("Maximum Total Return for Bad Category:", optimal_bad_threshold_rf$total_return))## [1] "Maximum Total Return for Bad Category: 33.42"print(paste("Maximum Total Profit for Bad Category:", optimal_bad_threshold_rf$total_profit))## [1] "Maximum Total Profit for Bad Category: 26.42"# Calculate total and average return and profit for the Bad category
total_return_rf_bad <- sum(bad_rf_results$match_return, na.rm = TRUE)
average_return_rf_bad <- mean(bad_rf_results$match_return, na.rm = TRUE)
total_profit_rf_bad <- sum(bad_rf_results$profit, na.rm = TRUE)
average_profit_rf_bad <- mean(bad_rf_results$profit, na.rm = TRUE)
# Print results for the Bad category
print(paste("Total Return for Bad Category (RF):", total_return_rf_bad))## [1] "Total Return for Bad Category (RF): 35.52"print(paste("Average Return per Bad Category Match (RF):", average_return_rf_bad))## [1] "Average Return per Bad Category Match (RF): 1.07636363636364"print(paste("Total Profit for Bad Category (RF):", total_profit_rf_bad))## [1] "Total Profit for Bad Category (RF): 28.52"print(paste("Average Profit per Bad Category Match (RF):", average_profit_rf_bad))## [1] "Average Profit per Bad Category Match (RF): 0.864242424242424"good_test_target <- as.numeric(as.character(good_test_data_filtered$result))
good_test_features <- good_test_data_filtered[, !names(good_test_data_filtered) %in% "result"]
good_test_features <- good_test_features[, !names(good_test_features) %in% "category"]
good_test_matrix <- xgb.DMatrix(data = as.matrix(good_test_features), label = good_test_target)
medium_test_target <- as.numeric(as.character(medium_test_data_filtered$result))
medium_test_features <- medium_test_data_filtered[, !names(medium_test_data_filtered) %in% "result"]
medium_test_features <- medium_test_features[, !names(medium_test_features) %in% "category"]
medium_test_matrix <- xgb.DMatrix(data = as.matrix(medium_test_features), label = medium_test_target)
bad_test_target <- as.numeric(as.character(bad_test_data_filtered$result))
bad_test_features <- bad_test_data_filtered[, !names(bad_test_data_filtered) %in% "result"]
bad_test_features <- bad_test_features[, !names(bad_test_features) %in% "category"]
bad_test_matrix <- xgb.DMatrix(data = as.matrix(bad_test_features), label = bad_test_target)params2 <- list(
objective = "multi:softprob",
num_class = 3,
eval_metric = "merror",
eta = 0.05,
max_depth = 3,
nthread = 2
)
num_round <- 100
model_good_prob <- xgb.train(
params = params2,
data = good_matrix,
nrounds = num_round
)
model_medium_prob <- xgb.train(
params = params2,
data = medium_matrix,
nrounds = num_round
)
model_bad_prob <- xgb.train(
params = params2,
data = bad_matrix,
nrounds = num_round
)good_predictions_xg <- predict(model_good, newdata = good_test_matrix)
medium_predictions_xg <- predict(model_medium, newdata = medium_test_matrix)
bad_predictions_xg <- predict(model_bad, newdata = bad_test_matrix)pred_probs_good_xg <- predict(model_good_prob, newdata = good_test_matrix, type = "prob")
pred_probs_medium_xg <- predict(model_medium_prob, newdata = medium_test_matrix, type = "prob")
pred_probs_bad_xg <- predict(model_bad_prob, newdata = bad_test_matrix, type = "prob")pred_probs_good_xg <- matrix(pred_probs_good_xg, ncol = 3, byrow = TRUE)
colnames(pred_probs_good_xg) <- c("0", "1", "2")
pred_probs_bad_xg <- matrix(pred_probs_bad_xg, ncol = 3, byrow = TRUE)
colnames(pred_probs_bad_xg) <- c("0", "1", "2")
pred_probs_medium_xg <- matrix(pred_probs_medium_xg, ncol = 3, byrow = TRUE)
colnames(pred_probs_medium_xg) <- c("0", "1", "2")good_test_matrix <- xgb.DMatrix(data = as.matrix(good_test_features))
preds_good_test <- predict(model_good, good_test_matrix)
conf_matrix_good_test <- confusionMatrix(
as.factor(preds_good_test),
as.factor(good_test_target)
)
cat("\n-- Good Category TEST --\n")##
## -- Good Category TEST --print(conf_matrix_good_test)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 3 3 1
## 1 3 11 2
## 2 7 2 9
##
## Overall Statistics
##
## Accuracy : 0.561
## 95% CI : (0.3975, 0.7153)
## No Information Rate : 0.3902
## P-Value [Acc > NIR] : 0.01984
##
## Kappa : 0.3399
##
## Mcnemar's Test P-Value : 0.21229
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.23077 0.6875 0.7500
## Specificity 0.85714 0.8000 0.6897
## Pos Pred Value 0.42857 0.6875 0.5000
## Neg Pred Value 0.70588 0.8000 0.8696
## Prevalence 0.31707 0.3902 0.2927
## Detection Rate 0.07317 0.2683 0.2195
## Detection Prevalence 0.17073 0.3902 0.4390
## Balanced Accuracy 0.54396 0.7438 0.7198conf_matrix_good_xg <- confusionMatrix(as.factor(good_predictions_xg), as.factor(good_test_data_filtered$result))
print(conf_matrix_good_xg)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 3 3 1
## 1 3 11 2
## 2 7 2 9
##
## Overall Statistics
##
## Accuracy : 0.561
## 95% CI : (0.3975, 0.7153)
## No Information Rate : 0.3902
## P-Value [Acc > NIR] : 0.01984
##
## Kappa : 0.3399
##
## Mcnemar's Test P-Value : 0.21229
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.23077 0.6875 0.7500
## Specificity 0.85714 0.8000 0.6897
## Pos Pred Value 0.42857 0.6875 0.5000
## Neg Pred Value 0.70588 0.8000 0.8696
## Prevalence 0.31707 0.3902 0.2927
## Detection Rate 0.07317 0.2683 0.2195
## Detection Prevalence 0.17073 0.3902 0.4390
## Balanced Accuracy 0.54396 0.7438 0.7198conf_matrix_medium_xg <- confusionMatrix(as.factor(medium_predictions_xg), as.factor(medium_test_data_filtered$result))
print(conf_matrix_medium_xg)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 1 4 1
## 1 4 6 4
## 2 2 4 7
##
## Overall Statistics
##
## Accuracy : 0.4242
## 95% CI : (0.2548, 0.6078)
## No Information Rate : 0.4242
## P-Value [Acc > NIR] : 0.5663
##
## Kappa : 0.0978
##
## Mcnemar's Test P-Value : 0.9536
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.1429 0.4286 0.5833
## Specificity 0.8077 0.5789 0.7143
## Pos Pred Value 0.1667 0.4286 0.5385
## Neg Pred Value 0.7778 0.5789 0.7500
## Prevalence 0.2121 0.4242 0.3636
## Detection Rate 0.0303 0.1818 0.2121
## Detection Prevalence 0.1818 0.4242 0.3939
## Balanced Accuracy 0.4753 0.5038 0.6488conf_matrix_bad_xg <- confusionMatrix(as.factor(bad_predictions_xg), as.factor(bad_test_data_filtered$result))
print(conf_matrix_bad_xg)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1 2
## 0 0 0 1
## 1 3 23 3
## 2 1 0 2
##
## Overall Statistics
##
## Accuracy : 0.7576
## 95% CI : (0.5774, 0.8891)
## No Information Rate : 0.697
## P-Value [Acc > NIR] : 0.2912
##
## Kappa : 0.34
##
## Mcnemar's Test P-Value : 0.1116
##
## Statistics by Class:
##
## Class: 0 Class: 1 Class: 2
## Sensitivity 0.0000 1.0000 0.33333
## Specificity 0.9655 0.4000 0.96296
## Pos Pred Value 0.0000 0.7931 0.66667
## Neg Pred Value 0.8750 1.0000 0.86667
## Prevalence 0.1212 0.6970 0.18182
## Detection Rate 0.0000 0.6970 0.06061
## Detection Prevalence 0.0303 0.8788 0.09091
## Balanced Accuracy 0.4828 0.7000 0.64815good_xg_results <- good_test_data_filtered %>%
mutate(
predicted_result = good_predictions_xg,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Good category
good_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Good category
good_results_xg <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Good category
for (good_thresh in good_thresholds) {
good_results_filtered <- good_test_data_filtered %>%
mutate(
predicted_result_good = good_predictions_xg,
predicted_prob_good = case_when(
predicted_result_good == 1 ~ pred_probs_good_xg[, "1"],
predicted_result_good == 2 ~ pred_probs_good_xg[, "2"],
predicted_result_good == 0 ~ pred_probs_good_xg[, "0"],
TRUE ~ NA_real_
),
match_return_good = case_when(
predicted_prob_good < good_thresh ~ 0, # No bet if below threshold
predicted_result_good == 1 & result == 1 ~ X1,
predicted_result_good == 2 & result == 2 ~ X2,
predicted_result_good == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_good = case_when(
predicted_prob_good < good_thresh ~ 0, # No bet if below threshold
match_return_good > 0 ~ match_return_good,
TRUE ~ -1
)
)
# Calculate total return and profit for the Good category
total_return_good <- sum(good_results_filtered$match_return_good, na.rm = TRUE)
total_profit_good <- sum(good_results_filtered$profit_good, na.rm = TRUE)
# Store results for this threshold
good_results_xg <- rbind(
good_results_xg,
data.frame(threshold = good_thresh, total_return = total_return_good, total_profit = total_profit_good)
)
}
# Find the threshold with the highest total profit for the Good category
optimal_good_threshold_xg <- good_results_xg[which.max(good_results_xg$total_profit), ]
# Print the results
print(good_results_xg)## threshold total_return total_profit
## 1 0.50 14.33 5.33
## 2 0.51 14.33 6.33
## 3 0.52 14.33 7.33
## 4 0.53 12.83 5.83
## 5 0.54 12.83 5.83
## 6 0.55 12.83 5.83
## 7 0.56 12.83 5.83
## 8 0.57 12.83 5.83
## 9 0.58 10.33 4.33
## 10 0.59 10.33 4.33
## 11 0.60 8.83 4.83
## 12 0.61 8.83 5.83
## 13 0.62 8.83 6.83
## 14 0.63 8.83 6.83
## 15 0.64 7.11 6.11
## 16 0.65 7.11 6.11
## 17 0.66 5.71 4.71
## 18 0.67 4.55 3.55
## 19 0.68 4.55 3.55
## 20 0.69 4.55 3.55
## 21 0.70 4.55 3.55
## 22 0.71 4.55 4.55
## 23 0.72 4.55 4.55
## 24 0.73 4.55 4.55
## 25 0.74 4.55 4.55
## 26 0.75 4.55 4.55
## 27 0.76 4.55 4.55
## 28 0.77 4.55 4.55
## 29 0.78 4.55 4.55
## 30 0.79 3.39 3.39
## 31 0.80 3.39 3.39
## 32 0.81 1.10 1.10
## 33 0.82 1.10 1.10
## 34 0.83 1.10 1.10
## 35 0.84 1.10 1.10
## 36 0.85 1.10 1.10
## 37 0.86 0.00 0.00
## 38 0.87 0.00 0.00
## 39 0.88 0.00 0.00
## 40 0.89 0.00 0.00
## 41 0.90 0.00 0.00print(paste("Optimal Threshold for Good Category (XGBoost):", optimal_good_threshold_xg$threshold))## [1] "Optimal Threshold for Good Category (XGBoost): 0.52"print(paste("Maximum Total Return for Good Category (XGBoost):", optimal_good_threshold_xg$total_return))## [1] "Maximum Total Return for Good Category (XGBoost): 14.33"print(paste("Maximum Total Profit for Good Category (XGBoost):", optimal_good_threshold_xg$total_profit))## [1] "Maximum Total Profit for Good Category (XGBoost): 7.33"total_return_xg_good <- sum(good_xg_results$match_return, na.rm = TRUE)
average_return_xg_good <- mean(good_xg_results$match_return, na.rm = TRUE)
total_profit_xg_good <- sum(good_xg_results$profit, na.rm = TRUE)
average_profit_xg_good <- mean(good_xg_results$profit, na.rm = TRUE)
print(paste("Total Return for Good Category (XG):", total_return_xg_good))## [1] "Total Return for Good Category (XG): 48.02"print(paste("Average Return per Good Category Match (XG):", average_return_xg_good))## [1] "Average Return per Good Category Match (XG): 1.17121951219512"print(paste("Total Profit for Good Category (XG):", total_profit_xg_good))## [1] "Total Profit for Good Category (XG): 30.02"print(paste("Average Profit per Good Category Match (XG):", average_profit_xg_good))## [1] "Average Profit per Good Category Match (XG): 0.732195121951219"medium_xg_results <- medium_test_data_filtered %>%
mutate(
predicted_result = medium_predictions_xg,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Medium category
medium_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Medium category
medium_results_xg <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Medium category
for (medium_thresh in medium_thresholds) {
medium_results_filtered <- medium_test_data_filtered %>%
mutate(
predicted_result_medium = medium_predictions_xg,
predicted_prob_medium = case_when(
predicted_result_medium == 1 ~ pred_probs_medium_xg[, "1"],
predicted_result_medium == 2 ~ pred_probs_medium_xg[, "2"],
predicted_result_medium == 0 ~ pred_probs_medium_xg[, "0"],
TRUE ~ NA_real_
),
match_return_medium = case_when(
predicted_prob_medium < medium_thresh ~ 0, # No bet if below threshold
predicted_result_medium == 1 & result == 1 ~ X1,
predicted_result_medium == 2 & result == 2 ~ X2,
predicted_result_medium == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_medium = case_when(
predicted_prob_medium < medium_thresh ~ 0, # No bet if below threshold
match_return_medium > 0 ~ match_return_medium,
TRUE ~ -1
)
)
# Calculate total return and profit for the Medium category
total_return_medium <- sum(medium_results_filtered$match_return_medium, na.rm = TRUE)
total_profit_medium <- sum(medium_results_filtered$profit_medium, na.rm = TRUE)
# Store results for this threshold
medium_results_xg <- rbind(
medium_results_xg,
data.frame(threshold = medium_thresh, total_return = total_return_medium, total_profit = total_profit_medium)
)
}
# Find the threshold with the highest total profit for the Medium category
optimal_medium_threshold_xg <- medium_results_xg[which.max(medium_results_xg$total_profit), ]
# Print the results
print(medium_results_xg)## threshold total_return total_profit
## 1 0.50 13.76 9.76
## 2 0.51 11.81 7.81
## 3 0.52 11.81 7.81
## 4 0.53 9.86 5.86
## 5 0.54 9.86 5.86
## 6 0.55 9.86 5.86
## 7 0.56 8.58 4.58
## 8 0.57 7.22 4.22
## 9 0.58 7.22 4.22
## 10 0.59 7.22 4.22
## 11 0.60 7.22 4.22
## 12 0.61 7.22 4.22
## 13 0.62 7.22 4.22
## 14 0.63 7.22 4.22
## 15 0.64 7.22 4.22
## 16 0.65 7.22 4.22
## 17 0.66 7.22 4.22
## 18 0.67 7.22 5.22
## 19 0.68 7.22 5.22
## 20 0.69 7.22 6.22
## 21 0.70 7.22 6.22
## 22 0.71 7.22 6.22
## 23 0.72 7.22 6.22
## 24 0.73 7.22 6.22
## 25 0.74 7.22 6.22
## 26 0.75 5.89 4.89
## 27 0.76 4.56 3.56
## 28 0.77 4.56 3.56
## 29 0.78 3.20 2.20
## 30 0.79 1.80 0.80
## 31 0.80 1.80 0.80
## 32 0.81 0.00 -1.00
## 33 0.82 0.00 -1.00
## 34 0.83 0.00 -1.00
## 35 0.84 0.00 -1.00
## 36 0.85 0.00 0.00
## 37 0.86 0.00 0.00
## 38 0.87 0.00 0.00
## 39 0.88 0.00 0.00
## 40 0.89 0.00 0.00
## 41 0.90 0.00 0.00print(paste("Optimal Threshold for Medium Category (XGBoost):", optimal_medium_threshold_xg$threshold))## [1] "Optimal Threshold for Medium Category (XGBoost): 0.5"print(paste("Maximum Total Return for Medium Category (XGBoost):", optimal_medium_threshold_xg$total_return))## [1] "Maximum Total Return for Medium Category (XGBoost): 13.76"print(paste("Maximum Total Profit for Medium Category (XGBoost):", optimal_medium_threshold_xg$total_profit))## [1] "Maximum Total Profit for Medium Category (XGBoost): 9.76"# Calculate total and average return and profit for the Medium category
total_return_xg_medium <- sum(medium_xg_results$match_return, na.rm = TRUE)
average_return_xg_medium <- mean(medium_xg_results$match_return, na.rm = TRUE)
total_profit_xg_medium <- sum(medium_xg_results$profit, na.rm = TRUE)
average_profit_xg_medium <- mean(medium_xg_results$profit, na.rm = TRUE)
# Print results for the Medium category
print(paste("Total Return for Medium Category (XG):", total_return_xg_medium))## [1] "Total Return for Medium Category (XG): 25.16"print(paste("Average Return per Medium Category Match (XG):", average_return_xg_medium))## [1] "Average Return per Medium Category Match (XG): 0.762424242424242"print(paste("Total Profit for Medium Category (XG):", total_profit_xg_medium))## [1] "Total Profit for Medium Category (XG): 6.16"print(paste("Average Profit per Medium Category Match (XG):", average_profit_xg_medium))## [1] "Average Profit per Medium Category Match (XG): 0.186666666666667"bad_xg_results <- bad_test_data_filtered %>%
mutate(
predicted_result = bad_predictions_xg,
match_return = case_when(
predicted_result == 1 & result == 1 ~ X1,
predicted_result == 2 & result == 2 ~ X2,
predicted_result == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit = case_when(
match_return > 0 ~ match_return,
TRUE ~ -1
)
)# Define a range of thresholds to test for the Bad category
bad_thresholds <- seq(0.50, 0.90, by = 0.01)
# Initialize an empty data frame to store results for the Bad category
bad_results_xg <- data.frame(threshold = numeric(), total_return = numeric(), total_profit = numeric())
# Loop over each threshold and calculate return and profit for the Bad category
for (bad_thresh in bad_thresholds) {
bad_results_filtered <- bad_test_data_filtered %>%
mutate(
predicted_result_bad = bad_predictions_xg,
predicted_prob_bad = case_when(
predicted_result_bad == 1 ~ pred_probs_bad_xg[, "1"],
predicted_result_bad == 2 ~ pred_probs_bad_xg[, "2"],
predicted_result_bad == 0 ~ pred_probs_bad_xg[, "0"],
TRUE ~ NA_real_
),
match_return_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0, # No bet if below threshold
predicted_result_bad == 1 & result == 1 ~ X1,
predicted_result_bad == 2 & result == 2 ~ X2,
predicted_result_bad == 0 & result == 0 ~ X,
TRUE ~ 0
),
profit_bad = case_when(
predicted_prob_bad < bad_thresh ~ 0, # No bet if below threshold
match_return_bad > 0 ~ match_return_bad,
TRUE ~ -1
)
)
# Calculate total return and profit for the Bad category
total_return_bad <- sum(bad_results_filtered$match_return_bad, na.rm = TRUE)
total_profit_bad <- sum(bad_results_filtered$profit_bad, na.rm = TRUE)
# Store results for this threshold
bad_results_xg <- rbind(
bad_results_xg,
data.frame(threshold = bad_thresh, total_return = total_return_bad, total_profit = total_profit_bad)
)
}
# Find the threshold with the highest total profit for the Bad category
optimal_bad_threshold_xg <- bad_results_xg[which.max(bad_results_xg$total_profit), ]
# Print the results
print(bad_results_xg)## threshold total_return total_profit
## 1 0.50 30.99 24.99
## 2 0.51 30.99 26.99
## 3 0.52 29.33 25.33
## 4 0.53 27.72 23.72
## 5 0.54 27.72 23.72
## 6 0.55 25.62 22.62
## 7 0.56 25.62 22.62
## 8 0.57 24.01 21.01
## 9 0.58 24.01 21.01
## 10 0.59 24.01 21.01
## 11 0.60 22.40 19.40
## 12 0.61 22.40 19.40
## 13 0.62 22.40 19.40
## 14 0.63 22.40 19.40
## 15 0.64 22.40 19.40
## 16 0.65 22.40 19.40
## 17 0.66 22.40 19.40
## 18 0.67 22.40 19.40
## 19 0.68 22.40 19.40
## 20 0.69 22.40 19.40
## 21 0.70 21.10 18.10
## 22 0.71 19.88 16.88
## 23 0.72 19.88 17.88
## 24 0.73 19.88 18.88
## 25 0.74 19.88 18.88
## 26 0.75 18.68 17.68
## 27 0.76 13.46 12.46
## 28 0.77 13.46 12.46
## 29 0.78 13.46 12.46
## 30 0.79 11.06 10.06
## 31 0.80 11.06 10.06
## 32 0.81 9.90 8.90
## 33 0.82 7.35 6.35
## 34 0.83 6.23 5.23
## 35 0.84 5.21 4.21
## 36 0.85 5.21 4.21
## 37 0.86 4.20 3.20
## 38 0.87 4.20 3.20
## 39 0.88 4.20 3.20
## 40 0.89 4.20 3.20
## 41 0.90 4.20 3.20print(paste("Optimal Threshold for Bad Category (XGBoost):", optimal_bad_threshold_xg$threshold))## [1] "Optimal Threshold for Bad Category (XGBoost): 0.51"print(paste("Maximum Total Return for Bad Category (XGBoost):", optimal_bad_threshold_xg$total_return))## [1] "Maximum Total Return for Bad Category (XGBoost): 30.99"print(paste("Maximum Total Profit for Bad Category (XGBoost):", optimal_bad_threshold_xg$total_profit))## [1] "Maximum Total Profit for Bad Category (XGBoost): 26.99"# Calculate total and average return and profit for the Bad category
total_return_xg_bad <- sum(bad_xg_results$match_return, na.rm = TRUE)
average_return_xg_bad <- mean(bad_xg_results$match_return, na.rm = TRUE)
total_profit_xg_bad <- sum(bad_xg_results$profit, na.rm = TRUE)
average_profit_xg_bad <- mean(bad_xg_results$profit, na.rm = TRUE)
# Print results for the Bad category
print(paste("Total Return for Bad Category (XG):", total_return_xg_bad))## [1] "Total Return for Bad Category (XG): 33.86"print(paste("Average Return per Bad Category Match (XG):", average_return_xg_bad))## [1] "Average Return per Bad Category Match (XG): 1.02606060606061"print(paste("Total Profit for Bad Category (XG):", total_profit_xg_bad))## [1] "Total Profit for Bad Category (XG): 25.86"print(paste("Average Profit per Bad Category Match (XG):", average_profit_xg_bad))## [1] "Average Profit per Bad Category Match (XG): 0.783636363636364"